The rating of a single grade oil (i.e. SAE 30) indicates a scale of the viscosity of that oil at 100 degrees C (212 F.) The higher the number, the higher the viscosity. higher number = "thicker"
If there is a 'W,' (i.e. 20W), that means it tests to that viscosity at a winter temperature as well as 100 degrees C. The colder oil gets, the higher it's viscosity is. Simply grading the oil at 20W does not make it multi-grade.
Multi-grade oils have additives to improve the viscosity index. A 10W-30, for example, will pump at cold temperature as well as a single grade 10 weight, and in addition exhibits the viscosity of a 30 weight oil at 100 degrees C. These multi-grade oils still change fairly significantly over temperature, but to a lesser degree than the single grades.