Let's game up a definitive definition of Taijiquan today. In one sentence I will summarize the one goal and the primary means of achieving that goal.
Taijiquan is a method whereby absolute relaxation of mind and body are used to create and enhance the internal energetic connection from feet to fingers.
That's all you really need. to know. It covers both the energy cultivation aspect and the primary configuration for combative deployment. It is in full accordance with the essential points of the Taiji classic writings (that is just a footnote. Such conformance won't matter much to you once you actually begin to experience the unspeakable energy surge of advanced Taiji, but for you beginners out there or for those who've practiced many years without really getting anything, that conformance to the Classics will be reassuring.) This defintion also distinguishes Taiji from, on the one hand:
(a) all other forms of martial arts which no matter what they may say, uniformally rely on some form of physical tension, mechanical structure, or anatomically based technique, and, on the other hand, from:
(b) the myriad of hand-waving qi gong frameworks and brands out there, as well as their cousin systems of more sendentary or meditative Taoist energy cultivation methods.
Taiji is really something absolutely unique.
One thing that sometimes strikes and bedevils smarter people who look into Taiji is the apparent contradiction between the conventional Taiji adages, both of which are found in the Classic writings:
i. the qi sinks to the navel
ii. the power rises from feet to fingers
If the "qi" is actually the "power", then what gives with this? Is the qi power going up or down or what? In fact, this is not a contradiction. The difference is between phases. In cultivation, you relax body and mind absolutely which results in the scattered floating qi of the shoulders and upper body concentrating at the navel. In deployment, the applied qi or "jing" power resulting from whole body qi permeation is grounded in the feet and is expressed through the body and out from the hands.
If you haven't felt this as an absolute unmistakable overwhelming concrete reality then though you've heard the words you've never felt the music, believe me. But possibly someday you will if you ever manage to grope onto a viable Taiji training system (of which there are few since most systems do not have relaxation as their primary goal - they are focused mainly on performance or maintenance of lineage and tradition, or being easy on your body, or physically working your body, or any of a thousand other irrelevant non-Taiji considerations).
Anyway, as I was saying, if you are really advanced and have the energy connection running then of course you know all about the torrential flood of sparky radioactive/electromagnetic pulse energy that surges in a continuous mind-blowing eruption from feet to fingers, whenever you will it to be so. And you can also feel the concentration of energy into the hara/tanden in the cultivation phase of course, that's even easier.
But what many people, even advanced practitioners have rarely felt is the last stage of "sinking" whereby the energy drifts down to the feet, whence it rises again in the deployment process already discussed. In fact, the more advanced you become the less likely you'll ever feel that downward current per se because over time the energy manifestation overall becomes more "state" like (full bottle of vinegar) as opposed to partial flow (though both modes are always accessible, just a light can be observed as a particle or as a wave).
It's not necessary to ever call out that downward drift phenomenon for explicit experiencinng, yet it can be fun if you know how to do it. That's today's TCGS bonus for you. (Note this is not a Taiji development exercise, merely a fun occasional "diagnostic" thing.)
The way to have an explicit experience of that is to get into the yoga pose Sirsasana (basic headstand). Key thing is to have your feet completely straight and toes pointed straight up. You want to be as relaxed as you can (given the need to maintain some yoga structure). Obviously this is yoga and it's ok to be as "structural" and "tense" as needed to keep the right shape (but not more).
You should look like this:

... or even point your toes straighter than above. (It's like Beautiful Lady's Foot ahahaha!)
Anyway not like this:

Now that you've got it up, the fun part:
if you focus your mind on your feet and toes, and relax the lumbar region as much as possible compatible with holding the fully correct shape, you will experience the 'topographically' upward flow of the energy as a fantastic sparky torrent from lumbar region to tips of toes. (It'll really freak you out if you haven't felt that before, it's like a strong electric shock minus pain, so don't get overly distracted and crash out of your pose!)
This is what is happening all the time in correct Taiji practice, prior to the "feet to fingers" deployment phase, this is the next stage of "sinking" after tanden concentration. But normally it's hard to feel it concretely when fully upright. (Of course the 'feet to fingers' deployment phase is fully experience in mind blowing surges as described earlier in this post). So in the headstand it's 'topographically' upwards but 'anatomically' downwards, weird but incredibly fun, enjoy.
Conversely, if you do the Sirsasana correctly but don't feel this upward/downward electric surge, that means your Taiji just isn't there yet. Probably your method of TC doesn't really prioritize relaxation, just lip service as they covertly pursue other goals like performance orientation, tradition or lineage fealty, physical fitness, or just plain making tuition money, etc. That's not Taiji, but anyway keep yer nose to the grindstone.