[Crystal Ambassador]

There are a few different things going on during massage, and by far the biggest reason is what you mentioned; it helps relax muscles. This is helpful for what the previous commenter stated, that many people are stuck in the "fight or flight" stress response and can't fully or easily relax. In this case, massage - especially massage that uses light pressure with slow, smooth hand movements - can help someone have some time in a safe, quiet, comfortable space. This can particularly help people who are suffering from touch deprivation, which - in a nutshell - is the experience of rarely receiving nurturing physical touch. People who are elderly or live alone often suffer from this. It can also help those who have been victims of sexual or other physical abuse; in massage, a client who has experienced physical abuse is presented with the opportunity to be in a vulnerable place and experience touch that is nurturing and intimate without requesting anything from them sexually or violating their boundaries. It allows them to re-experience the possibility that touch can once again be affiliated with healing, and not just used to bring them harm.

For deep tissue work, that often works more on the physical level. Basically how muscles work is this; when the brain needs to use a muscle (ie, to pick something up), it sends a nutrient to the muscle that causes it to contract/tense up. When that muscle is no longer needed, the brain stops sending the nutrient and sends a different nutrient that causes relaxation. Now when a muscle feels that it is being stretched too far, it will also contract to offset the pulling force and keep the muscle fibers from tearing. Oftentimes if a brain believes it's about to have its muscles pulled too far and torn (such as if it sees it's about to be struck by a car), it will pre-emptively contract them for protection. Many people have stressful lives, and their brain reads the mental stress as being a sign of imminent physical harm. So it activates the pre-emptive protection response.

If someone is suffering from tense or sore muscles (which most people are), it can help relax them from a few different factors. The physical pressure of a massaging hand can cause therapeutic inflammation, which is an increase in blood circulation to the muscle which allows the muscle to receive the relaxation-causing nutrients.

Additionally, the sensation of touch causing an increase in soreness in the muscle helps alert the client's brain to the fact that the muscle is tense. Since a body at rest should automatically relax its muscles to allow for healing and prevent damage from overuse, the client's brain realizes that the muscle is still firing (and therefore not allowing it to heal), and will send a relaxation response to get it back to where it should be while at rest. On a more conscious level, it's common for a client not to know they have tense muscles in places like the front of the shoulders; by becoming aware of it, they can do things like stretch it to help it relax and recover.

If a client isn't able to get their tense muscles to relax on their own - such as not knowing exactly where the problem is starting from or how to apply pressure to get it to relax - it becomes helpful to go to someone who is more familiar with how the muscular system operates; a therapist. In this case the therapist can apply a deeper pressure that can either cut off circulation to it enough that it breaks the flow of the contraction-causing nutrient to the muscle or that manually stretches the muscle back into a relaxed length. A therapist can also explain why certain muscles are chronically sore, since they understand the intricate network and codependency of muscles and which ones affect each other. I'll explain:

The most common issue my clients come to me with is soreness and tension in their upper back, across the shoulderblades and up their neck, sometimes all the way up their scalp. This is most commonly seen in people who work at desks as well as hair-stylists, dental hygienists, welders, and other people who work by having their arms bent and reaching forward. The reason their shoulders/neck hurt so much is that in order to maintain their arms-bent, reaching-forward position, the muscles in their chest contract. These muscles work to pull the shoulders in the opposite direction of what the upper back/shoulderblades do, and so therefore are also stretching those upper back/shoulderblade muscles. Those muscles that are stretching then get stretched too far, and contract to prevent themselves from being torn (in the same manner as the person about to be struck by a car, but in this case the damaging force is the chest muscles constantly contracting). This position is also maintained when the person checks their phone, drives home, and - often - in how they sleep. So pretty much all the time, the chest muscles are pulling on the shoulders, causing them to try to counteract the damaging strength of the chest muscles.

What I do in this case is inform the client that their front shoulder and chest muscles are causing this problem (most people aren't aware of any pain/soreness in that area but become aware of it when it's worked on by a therapist), bring them awareness of how their position is causing that muscle issue, and then work on stopping the contraction of the front shoulder muscles. Then I move to the upper back/shoulderblade muscles which can safely and more thoroughly relax now that the chest muscles aren't pulling them. This allows them to finally get a chance to heal and rest.
Afterward clients usually feel a lot more flexibility and a lot less pain in their upper torso/shoulders/neck area, because the muscles of their upper torso are relaxed, flexible, and not being torn.
Of course this isn't exclusive to shoulder and neck pain, but the process is the same and can be applied to anywhere that is having an issue.

So basically, to summarize, the muscular system is like a bunch of rubber bands networked together. Some of those are pulled by others and become too tense, which then hurts, and the job of the massage therapist is to use their knowledge of that network to figure out which rubber bands are pulling on the hurting rubber bands, and make the pulling ones stop.