When you ``glance'' at something, you look at it very quickly and then look away. For example, when we get stuck with a bore, every once in a while, we glance at the clock or the watch. We don't keep looking at the clock/watch because we don't want to be rude. We take a quick look (glance) at the watch and turn our attention to the speaker - and pretend to be interested in what he is saying. A glance is intentional; you deliberately look in a particular direction.
Peter glanced at the headlines while waiting for the bus.
Jane glanced at her notes before entering the examination hall.
Amy glanced at the TV before returning to his crossword puzzle.
When you catch a ``glimpse'' of something, you catch a quick sight of it. For example, while you are in the jungle, you may catch a glimpse of a tiger. In other words, you see the tiger very briefly. You may or may not see it completely. In the case of glimpse, it is the object which appears before our eyes. In the case of glance, it is the eyes which go to the object.
I caught a glimpse of Ann in the crowded room. When Elizabeth turned his head to glance at the clock, we caught a glimpse of the girl who was with him.
We caught a glimpse of the girl who had won the quiz competition.