The convention was known for three famous compromise. name and explain each.

I am going to assume that you are talking about the Constitutional Convention that took place in Philadelphia on May 14, 1787. The three famous compromises that took place where: 

1) The Connecticut Compromise (A.K.A The Great Compromise)
This solved the problem of representation in congress. Because of the great compromise we have a bicameral congress. This means in the senate each states gets 2 representatives regardless of the size of that state. But, in the House Of Representatives each state receives representatives based on the population of that state. 

2. The Three Fifths Compromise:
This compromise came about to satisfy the southern states delegates. Southern delegates wanted slaves to count as a whole person for population purposes but, they didn't want them to receive any constitutional rights. The idea to count each slave as 3/5 of a person came about this meant that for every 5 enslaved persons it would count as 3 free persons. 

3) The trade compromise (Commerce Compromise) 

Northern interests wanted the government to be able to impose tariffs on goods in order to protect against foreign competition. However, the Southern states feared that tariffs on their goods would hurt the trade upon which they heavily relied. The compromise was for imports to be only allowed on imports from foreign countries and not exports from the US.