What is a handout? when would it be useful to use a handout?

A handout is a project or a worksheet handed out to students to do in class. (Mostly.) Right after finishing is a pretty good time to pass these out. For example, if you finished a lesson on the greatest common factor, it would be best to give a handout on greatest common factor so students can remember GCF better.

A handout is a physical demonstration usually sheets of information or flyers.

There are many examples of the use of handouts. Teachers may use pass out handouts of a study guide to students so each one has an individual sheet of knowledge. Handouts can also be used in presentations. A presenter might hand out handouts to the audience to help them get a little more introduced to the topic or learn more about the details throughout the presentation. 

Handouts can be very important in teacher's job when she introduces a new topic or to a presenter when he/she tries to explain a significant and complex idea.