Yoga bandhas could be considered advanced practices when doing yoga poses. I first learned about them when doing ashtanga yoga but actually ceased to focus on them in order to focus on other aspects of yoga practice. As I began to improve my understanding of the body I found myself looking at them again, but this time from the view point of how they affect the tension network of the body.
So far in my understanding bandhas (or "locks") are like the tuning screws on a guitar, they can be used to vary tension in the body to make particular types of poses easier and more integrated.
(It also relates to control of the Lower Transverse Abdominis muscle.)
It is also known as the "root lock."
My own understanding of it is based on the idea that the pelvis is a flexible structure and root lock is one of the muscle actions that can be used to stabilize the pelvis as well as the SI Joint.
The amount of movement in the pelvis can be quite small but perceivable with the right amount of focus and muscle activity.
Because of the sensitivity required if you aren't even aware of your pelvis or have poor body awareness and control you may be better served by developing your awareness and control of the pelvis in simple movements like rocking it forwards and backwards. (That being said, you may find that trying to focus on something that is a little bit more challenging makes it easier to then develop an awareness of more gross (larger) movements of the body.)
In my understanding, mula bandha can be more than just activating the pelvic floor. It can also include activation of the muscles of the pelvic wall: obturator internus and externus as well as piriformis, iliacus and psoas.
All of these, except the obturator externus, form the inner border of the abdominal container. These may be the "true core" of the body, especially with respect to standing poses.
One reason for this rational is based on a basic idea of stability and muscle control, where a muscle requires one end or attachment to be stable so that it can relax, contract or otherwise act as desired. The overall term that I use for this is "control." With one end stable, i.e. one bone stable, a muscle is controllable whether subconsciously by the brain or in over ride mode where we consciously attempt to control it.
Standing on one leg with the above muscles of the hip activated, the pelvis is stable giving the spinal erector muscles, deep spine muscles and abdominal muscles a stable platform from which to act in a controlled fashion on the spine and ribcage (and from there the head.)
(Further stability and control is provided by the poly-articulate muscles that connect the pelvis to the lower leg.)
I'd suggest that when these muscles function well together (properly) you may well be on the way to alleviating SI joint problems, hip pain and possible low back pain.
There may be other factors but I'd suggest work on developing these muscles is a good starting point.
One of the reasons for contracting these muscles is that as well as stabilizing the hip joint they stabilize the lower half of the abdominal container. The upper half consists of the diaphragm and transverse abdominis, major muscles of respiration. It may be that with bottom half stable, the above two muscles can work more efficiently to drive respiration.
With the lower portion of the pelvis the diaphragm can be used to efficiently expand the transverse diaphragm and vice versa.
This isn't the only possible configuration but it may be a good starting point (or one possible starting point) for exploring breathing patterns.
Root lock can be thought of as the sitting bones moving inwards (as a result of the pelvic floor muscles engaging.) Moving the sitting bones outwards could be thought of as a reverse or anti-mula bandha. You can read more about this action in this acticle on the sacroiliac joint.
One bandha that is often considered subsidiary or secondary to mula bandha is uddiyana bandha.
Uddiyana bandha is generally a pulling in or toning of the lower belly.
Depending on how you activate mula bandha, uddiyana bandha can sometimes happen automatically as a result of mula bandha.
The part of the belly that I considered to be "the lower belly" is the part that is covered by a hand if you place the edge of one hand against the top of the pubic bone with the palm on the belly and the fingers pointing to the side. For myself this region ends about half way to the belly button.
Pulling in this portion of the belly, and keeping it pulled in is a function of the lower fibers of the transverse abdominis (and possibly the internal obliques)
A good way to develop control of the transverse abdominis is with an exercise called agni sara. (There are two exercises called Agni Sara. The link points to the second variation.)
Uddiyana bandha is translated or thought of as "flying upwards" where mula bandha is "root lock." In my experience the part that flies upwards, or is allowed to lengthen upwards when uddiyana bandha is engaged is the ribcage.
At a basic anatomic level, adding tension to the transverse abdominis, particularly the lower band of fibers, pulls the bottom of the rectus abdominis muscle inwards which in turn adds slack to the upper portion of this muscle. This then allows the sternum of the ribcage to move upwards, away from the pubic bone, in effect, "flying upwards."
And so when doing uddiyana bandha you may find that it is beneficial to focus on lengthening the ribs upwards, as you pull the lower belly in.
I associated the psoas with mula bandha just because it is a part of the wall of the abdominal container. (The transverse abdominis and diaphragm are also.) It supports the front of the spine and when active may help the lumbar spine to straighten by lengthening while staying active. You could think of it like a belay line that mountaineers use. Even as the lumbar spine straightens, the psoas allows this straightening by lengthening but still staying active. By doing so it supports the front of the lumbar spine.
And so because of this lengthening upwards of the lumbar spine, psoas activation could also be considered a part of uddiyana bandha.
The third bandha and possibly the one least often mentioned is jalandhara bandha.
Philosophically this bandha is likened to a net which captures the energy captured and sent upwards by mula and uddiyana.
It could be considered as the final action which "ties together" the body as a whole unifying it. Or it could simply be considered as an action that brings awareness to the neck.
The neck and head is often one of the primary adjustment points I use when adjusting yoga poses whether verbally or hands on. One of the simplest instructions to activate jalandhara bandha is to move the ears up and back away from the shoulders so that the back of the neck lengthens.
A slightly deeper instruction, with the chin tucked in, is to squeeze behind the wind pipe (but in front of the spine.) The deeper muscles of the neck that help to open the back of the neck is called longus colli.
It may be the counterpart of the psoas in that both muscles attach directly to the front of the spine.
Even though it can be difficult to activate this muscle, I still teach neck awareness as part of a breathing exercise especially for those who have a hard time breathing.
Jalandhara bandha could be either the first or last element in elongating the entire spine. In yoga postures where the spine is bent backwards the "connective tissue tension" that the bandhas create may be useful in supporting the spine. If the spine is supported, stable, you may find it easier to go deeper into your yoga posture with less effort and more importantly with less undue strain on the parts of the body.
However, to learn how to activate and feel the bandhas (as well as learning to feel when they are deactivated) I'd suggest that you practice moving slowly and smoothly with your awareness focused on the parts of the body that are moving. You may also find it helpful to do a simple standing meditation with your awareness focused on the relevant anatomy.