Input buffering has a couple different interpretations.
The most common type of input buffering is to time an ability with a long cast time so that you're channeling when you're exposed to cc or when you use another ability. You can see a great example of that in Jatt's Fight Breakdown video for the TSM vs CLG match in the 2016 North American Spring Split finals. It also lets you change the direction of some abilities by flashing during the cast time.
Caitlyn has some really long channel times and you can see a bunch of examples of input buffering from her.
The second type of input buffering is much less commonly heard about since it's pretty obvious. This kind of input buffering is basically just spamming an action so that it executes immediately as soon as you're in range. It's useful for things like timing Vayne's Condemn to cancel Trist/Kha jumps.
What you seem to be describing is animation cancelling (please do correct me if I'm wrong). Which is very important to many champions. For example, Renekton's W resets his AA timer and Tiamat active cancels his W animation which allows for a very fast burst of AA -> W -> Tiamat -> AA
. Another example is Riven's animation/AA cancelling on her Q: AA -> Q -> wiggle -> AA -> Q -> wiggle -> AA -> Q -> wiggle -> AA
.
In terms of detecting the input buffering behavior, it will simply feel like they're putting down damage/executing plays regardless of the cc you've applied.
Detecting animation cancelling is slightly more complex, but you'll notice very slight movements or rapid fire abilities mixed with autos. It's kind of vague, but you mostly just have to know what can be cancelled/what can cancel and be on the look out for that kind of setup in each of your matches.