In a Taijiquan (Tai Chi) class, the teacher will repeatedly remind the students to relax. If there isn’t any clarification on the meaning of relaxation, the students are at risk of becoming weaker, and not stronger, by going in the wrong direction.
There’s a missing link in this equation: the correct posture. Only when coupled with the correct posture, relaxation will result in stability and power.
Relaxation is crucial for Taijiquan (Tai Chi), because of the following reasons:

Distribution of power

Ultimately, we are looking to develop power in Taijiquan (Tai Chi) – but power distribution is a key concept here. The human body is enormously adaptable in how it moves. Even under strenuous artificial conditions it can find a way to balance and compensate, and still be functional. The problem with the compensations is that they are not “planned” for the long term, they are in-the-moment solutions that the body devises instinctively, and often lead to decreased function and pain, after time. It is common that athletes and performers suffer a lot of pain and injuries, as their goals are records or beauty.
Take an individual who injures a knee ligament, for example. He might shift the distribution of effort in the hips to redirect it away from the hurt area, and the new power distribution will stick for all is life – and he could still be a good athlete, as we often see. The point here is that his muscles are working in a significantly different way than before the injury, and he is still functioning. It happens to us all, athletes or not: we adapt to injuries, to working conditions, or to common usage of our bodies.
The question asked in Taijiquan (Tai Chi) is: What if one wants to reclaim the natural, optimal way to distribute effort and transmit power in his body? It’s not effective to tell that person to use the body in one way or another. Many unconscious processes take place beyond his control. It can be of limited use to strengthen a muscle group that was weakened by the new movement pattern, but this approach doesn’t deal with whole-body movement, so it isn’t used in Taijiquan (Tai Chi).
According to Taijiquan (Tai Chi) didactic, the most effective way to teach the body to distribute power according to its own natural way is to relax, and have a knowledgeable teacher correct your posture. When this process is repeated for a long enough time, the body will slowly reclaim the perfectly balanced power distribution it has.

Linking

Taijiquan (Tai Chi) sees the body as a wholesome unit. We didn’t evolve as a group of separate muscles working together in unison. Seeing our bodies as being a collection of bones and muscles tied up together is limiting to both the body itself and the mind. Leading therapists are starting to preach that we should see the body as tough it were one single muscle-sac, with bones floating inside it, in a tensegrity structure. But they don’t yet have a movement system born from this vision.
Taijiquan (Tai Chi) provides a means to see, and most importantly to move the body as one integrally connected unity. That is what we call linking, and that can only be achieved through relaxation.

Feeling

We are used to thinking that we have five senses, but there exists another sense: Proprioception. It is the feeling of one’s body. Medical science has shown we have special neuronal sensors for that. When we tense up our bodies, we numb the feeling of pain – which can be useful – but we also drastically reduce the precision of our Proprioception, and loose the feeling of oneness.
The antidote for that is relaxation. Only by deeply relaxing we can learn to feel deep in our bodies and joints. However, one shouldn’t search for “Qi feelings” when doing Taijiquan (Tai Chi).

Following the center

Finally, to be able to obey the governing movement principle in Taijiquan (Tai Chi), we must relax and surrender control of the arms and legs to the center of the body. As long as we try to do this or that with our extremities, the whole body will not be following the movement of the center.
We have to learn how to relax all parts of the body, so they can feel the center leading, and follow it.

It is not enough to know this. Relaxation is a skill, and a skill cannot be copied. It has to be acquired through dedicated practice, that is the spirit of gogfu.