Giving points refers to the favorite in sports betting, which is the opposite of taking (receiving) points.
For example, if you bet the Bears as a -6.5 point favorite against the Lions, it means you're "giving six points" to the other team, as in the Lions are starting the game up 6-0. So in order to win the game and the bet, the Bears need to make up that ground, meaning if they score seven points and the Lions score zero, the final in the hypothetical game would be 7-6. In the real game, it would be 7-0, which also means they cover the -6.5 point spread as a favorite.
Since people use different phrases across the country, it's worth remembering "giving points" and "laying points" are the same thing.