In its most basic form, an Exemplification Paragraph is when you support a claim with many examples.
Here is an example. I'd like to be the teacher who could lend a hand. I'd be willing to help with school fundraisers and events. Some of the staff dislike staying after school to help with school fundraisers, but I believe that earning money for a good cause can be enjoyable. Some of the classroom activities in middle school were not particularly engaging.