To give (things of the same kind) to several people. When you distribute something to other people, you hand it out. Give out is similar to hand out.
Handing out free advice to all your friends will not make them like you.
At the Christmas party Santa Claus handed out the presents under the tree.
Emergency loan applications were handed out to the flood victims.
The teacher handed out the examination papers.
The teacher handed the tests out to the class.
The verbal idiom to hand out can be made into the noun handout to refer to items that are distributed in a class or meeting.
Alright, students, here are the class handouts for this week.