Relative:
=A1
When copied down it turns to =A2, =A3, =A4 etc
When copied right it turns to =B1, =C1, =D1
When copied diagonally it turns to =B2, =C3, =D4
It's great when copying formulas where the address needs to increase accordingly
Absolute:
=$A$1
No matter where or how you copy it, it will always read =$A$1
This is good when you need its cell reference to stay the same no matter where you copy it.
Mixed:
=$A1
In this case, No matter where you copy it, the reference to column A will always reference column A, but the row reference will increase with each row you copy down.
=A$1
In this case, No matter where you copy it, the reference to row 1 will always reference row 1, but the column reference will increase with each row you copy right.