How do balloons float?

The short story is, pure helium is lighter than the air around us. Helium is the second element on the periodic table, meaning it is the second smallest element by atomic weight. 

The air around us is mostly made up of nitrogen (80%) and oxygen (20%).  Both of these elements have a greater atomic weight than helium, and so are heavier.

Your helium filled balloon is filled with air that is lighter than the air around it, which forces it to float up up and away!  In the same way, oil is less dense (lighter) than water, so it will also float when surrounded by water.    

If you were to fill a balloon with just an air pump using the air around you, it would not float since the air in the balloon is equal (not lighter) to the air surrounding it.