To add my personal experience into this - during the Round Ireland race 2018 we had a front roll through overnight and it went like this. Boat was a J109.There are already some good replies to this above, technical and references etc. but I don't think anyone has answered the "what is it like crossing one on the water?" bit.
From my experience a few times, anything from "a bit rough" to "really horrible". When really horrible you can have pouring rain, wind increasing at an ever increasing pace until you wonder if it is possible for it to get any stronger, and it does. and the waves get huge and white. Then suddenly the wind can completely disappear and the sails go slack whilst the waves are bouncing the boat all over the place with the sails and boom banging about with no wind to hold them steady, threatening to break things and the sail, then suddenly the wind can come back from a totally different direction and at huge speed, so you don't know what tack to try and settle the boat, which can be completely stopped without steerage way at the time, onto, and you can also get hailstorms and sunshine at the same time. The big waves from different directions crash into each other so you can't really sense what direction they are coming from. After a short while, minutes to say half an hour, the wind usually settles down from a completely new direction and with reduced strength but it will still noy have a settled direction and may still have very strong gusts. Things then get better. It will be colder but the horrible confused state will gradually improve and the waves gradually settle down with a consistent new direction and a longer distance from peak to peak even though they can stay big for a long while. Sailing upwind into and through a strong cold front is not pleasant (at least not for me!) , but sailing across the wind in the conditions after I know I am through it are usually very good fun, with sunshine, white clouds with squalls under them, and fast sailing..
Well, more than one over a few days but this was the most memorable.
Night pretty calm, 10 knots breeze running under A2. I go down for an hour's kip.
I wake up to freezing cold, the boat is moving much, much faster and the trimmers are on deck calling out speeds, 12, 13, 14 knots.
Wind quickly builds to 30 knots+, we go off surfing up to 19 knots at times.
Go on deck to a very different scene to when I went below.
This sticks around for 40 mins or so.
Then breeze shuts off entirely, boat is left spinning on the currents, bobbing on the waves with severe rain for an hour until breeze fills in.
When it does fill in, it comes back at a nice leisurely 15 knots from a totally different direction and we're reaching on the opposite gybe.