Welcome to the boards, DonToo. May your travels in the Gael Serran keep boredom far away from you.
You've got the good answers already, but I would add one more thing: even though you're in training, you get the benefit of the new skill. For example, if you train in STR, your STR goes up immediately. You are then considered in training until the next time you level up.
That confused me originally, because I thought that I would get my strength point (or whatever) when I levelled up, and I didn't. I didn't realize that I'd already received it