As the first comment said, Rotation COULD refer to free champs for the week.
In-game, though, it tends to refer to a "rotation" for your team. As in you're grouped mid, you take the inner turret, then your team can "rotate" to top lane to take the turret there while you have the chance. Things like that.
"Pick" Refers to either the champion you select, OR (In-game) it can refer to catching someone out of place. As in their Morgana support wanders into your blue side jungle to get a deep ward right before a dragon fight, and you see her. Your team can collapse on her to "Pick" her off and turn the dragon battle into a 5v4.
They could both refer to other things as well, probably. But those are the most common uses I see for them.