As a system for the support and strengthening of the health of the body, emotions and mental faculties. This alone is motivation enough for many people, as the health benefits of Taiji are well recorded.
It can be said to be a system of martial expertise (and although the fighting side of the art is no longer essential in today's society, it is still an absolutely valid part of the art - and like the health aspect, is a natural consequence of good practice).
Taiji can be a means to explore and understand inner side of existence, to a degree that is only limited by you.
In practice, you can expect your understanding of the question 'What is Taiji?' to change as your quality and understanding of Taiji practice changes.
The typical experience is that one's understanding after a year of practice is quite different to that of a few months' practice. By the time three or so years are reached, it is different again. And after six or 10 years, understanding is different again. Each of these different understandings are not generally incompatible, but reflect the gathering depth of understanding and practice of the art.
After 14- 21 years of practice, one's understanding of the art entirely depends on how successful the practitioner has been in moving past the everyday mind, or the superficial mind as it is often referred to in the practice method of the Taiji School.
And here is the problem, (both with the question and all types of inner practice). Getting the superficial mind to explain things that it cannot truly appreciate (or as the practice gets more subtle - things it cannot perceive). I know the preceding sentence will cause resistance in many people as it's a common belief these days that the mind can comprehend pretty much anything and that it completely does our bidding (that one is a whole separate topic!), but I stand by the statement. Even better, prove it wrong (or right) to yourself!
This problem is due to the nature of this aspect of our common make up. There are depths to the practice that are beyond the reach of this part of the mind - it is as if it is a mechanical restriction of the body's make up. It shows itself as we come across these restrictions in the practice. But by a quirk of the superficial mind, it 'thinks' it knows all these things, because they have been heard or read about. And in doing so, becomes a very effective block to anyone looking to delve into these things.
But really - if you are still reading this far - you should just begin learning and practicing! If Taiji intrigues you, or you are otherwise attracted to it, you are best advised to stop learning about it - and begin doing it. All that Taiji has to offer is available only through the doing of the art. Theoretical knowledge of Taiji without the Taiji practice is empty and without foundation. And as Lao Tzu may say - misleading to man.
After some time of learning and practicing Taiji, you will know if it is for you or not. Unlike many activities, Taiji requires no significant financial investment - just your time, intelligence, motivation and effort. And its rewards are great - improving health of the body, emotions and mental faculties alone are huge benefits.
And having persevered this far, are you still looking for a brief easy explanation for 'What is Taiji?', perhaps you should be fulfilled in this wish. Taiji is everything. As Master Huang would often say 'There are no secrets in Taiji, just things too small for people to understand.' Taiji is the art of the increasingly subtle.
Around the age of 60, having practiced White Crane for over 20 years, and Taiji for around 25 years, he said he was just starting to understand Taiji. One begun, Taiji is best thought of as a lifetime practice. Its deeper aspects are not revealed without significant effective practice, its deep answers not understood, until the practice is deep enough to support the understanding.