This month's Airliner World has a helpful guide, which is better than I would have been able to describe in my own words!
-The right to overfly a country
-The right to make a technical stop in a country without collecting/dropping off traffic
-The right to carry traffic to a foreign country
-The right to carry traffic from a foreign country
-The right to carry traffic to a foreign country, then fly on to another country, with traffic rights on each sector
-The a type of fith freedom, but using the airline's base country as the transit point
In simple terms of an airline from country A operating flights to countries B and C.
Third Freedom would allow them to carry traffic from A to B, Fourth Freedom allows them to carry traffic from B to A. Fifth Freedom allows traffic to be carried on a route from A to B and on to C. Sixth Freedom allows a flight from B to A and on to C.
Hope that helped!