A lot of it falls to the level of braking pressure as well. We trail brake on the racetrack and it's a skill that also works well to tighten your line on the street, but to learn it is a bit tricky. Basically you CAN apply front brakes in a corner but we're talking about 5-8% only, more like "dragging" the brakes slightly since as Anubis stated if you overdo it, you pop upright.
Trail braking IS NOT using the rear brake. The term "trail" and "rear" have nothing in common in this instance. The fact that car racers talk about "trailing the brakes" into a turn has no relevance to motorcycles.
Trail braking is lightly dragging the front brake to keep the front end loaded slightly and the forks compressed. With most steering head rake set to about 23-24 degrees, as you compress forks you reduce the amount of trail and in essence shorten the bike's wheelbase.
We all know that short wheelbase bikes turn faster and easier but lack stability at high speed. Conversely, long wheelbase bikes make great drag bikes but suck at cornering. So by simply decreasing the wheelbase by several millimeters the bike will turn in quicker.
THIS HAS NOTHING to do with the "countersteering vs. body steering" debate. I have heard some uninformed people try to write off trail braking as a gimmick, yet Freddie Spencer can back up every thing he says with proven results. The bottom line is that a shorter wheelbase bike WILL in fact countersteer quicker. And we have seen a lot of people who brake only while upright struggle and fight to turn a bike in. Why? Because if you have the front compressed hard under heavy braking, and you come off the brakes quickly, the front is going to rebound quickly, and you can even INCREASE trail (lengthen wheelbase) and have your front end geometry out of whack at that point which makes the bike feel like it wants to run wide. Also, THIS can make you more prone to tucking the front as you have a sudden change (loss) of contact patch as you are trying to suddenly increase axial (cornering) demand if you try to "quick flick" the bike into the turn.
Some people seem to think that having the front loaded slightly means you have a higher chance of tucking the front. Perhaps...but you're not going to trail brake in off camber turns, on really dirty public roads, or hard downhill turns where the front is already heavily loaded. But a SLIGHT front load will increase the front tire's contact patch AND allow you to carry a higher corner entry speed since you are decelerating all the way to the apex, at which time you make a SMOOTH transition to throttle thus not unsettling the front/rear weight bias.
Learning to trail brake on the street is a very valuable skill. Not only do you finally understand that you CAN touch the front brakes while leaned over in a corner (to tighten your line if needed) but the bike actually does NOT have to stand up and run off the road just because you applied the front brakes. You can develop this skill to give you a LOT of confidence and control even when leaned over pretty far. In this shot, I'm trail braking fairly aggressively coming into T9 at Thunderhill:
Is there a limit to trail braking? Sure. You're perhaps more likely to tuck the front if you have too much front end load. But compared to the guy who brakes while upright and then tries to "throttle through the corner" you have a MUCH lower chance of losing the rear wheel and potentially high-siding. I tucked the front at Pahrump in June while trailing very deep into T1. But I know why it happened and I walked away without injury. Near 100 deg temps, super soft front race tire, trailing a bit too hard (front loaded to max) and then I crossed a pavement seam.
I recall Freddie telling a story of how KR and Barry Sheene would try to take him on the outside as he'd trail (since he'd actually be slightly slower at the apex) but then he was more upright and co