Transcendence is one of the goals of NonDirective Meditation. Technically it's when you move beyond thought, and you experience pure consciousness, and the act of doing this is called "Transcending".
Between the different teachers of NonDirective techniques, you'll find varying definitions of transcendence, with plenty of blurred lines.
To me, transcendence is the act of experiencing the movement back and fourth, from thought to the mantra, and the eventual emptiness, or lack of thought. The state we achieve here is also called "pure consciousness".
I think it's ok that the definitions are a bit skewed, and hard to get a grip on. Really, we're looking for the benefits when we meditate, the things we carry into our daily lives.
Transcendence is very enjoyable, and it does probably indicate that we are getting benefits that we'll carry into our daily lives, but not having the experience should not be something you worry about, because you will benefit a ton from NonDirective meditation before you actually "transcend".
In most definitions, transcendence is a state - where you don't have any thoughts, and you don't have any feelings, both physical and bodily - and you are completely aware, and present, and it's a great feeling.
So transcending is riding that wave - or the two strokes that are sometimes talked about, it's the act of being in the process of reaching transcendence.
This is my description - but I can say that when you achieve it (transcendence), you'll know it. You won't have to ask anyone if "that was it".