Meditation
What Is Meditation
Meditation is studying the Mind from within; Meditation is training the Mind from within.
We can see our Mind as a laboratory; we can see our Meditation as the performing of science experiments within that laboratory. We plan experiments, perform experiments, observe the results, and update our theories accordingly. In this way we learn how our Mind works, in time we reach the point where we may be said to know mind. (In the same way that, say, Albert Einstein could be said to 'know physics'.)
Spiritual Discipline
While Meditation needn't necessarily be considered a Spiritual Discipline, I'm of the view that it is best when it is. Spiritual Discipline is all about transforming oneself from within, bring body under the command of Mind, bringing Mind under the command of our conscious Self, and directive our lives, via the Mind, so as to live ethically, altruistically, and for the benefit of all, rather than just ourselves. It is in training oneself to live for the benefit of all that Meditation as a practice fully bears fruit. (Just practising Meditation because it feels nice, or helps you chill out, misses much of the point and benefit of a Meditative discipline.)
What is the Relationship Between Meditation and Taiji
Taiji is the study and training if Mind and Body from within. In Taiji we meditate upon Awareness, both spatial awareness and body sensations; In Taiji we deliberately direct our Intention with meditative focus; In Taiji we move our body by directing our Intention; In Taiji we train our brain in order that we move our body through Intention.
I suspect similar could be said of Yoga, but I lack the experience to comment. In short, Taiji is a meditative discipline. The slow 'arm-waving' exercises are part of a framework in which to practise this. I'll say more in the Taiji section of this wiki.