How can an air pump move water?

[Rachael94]

http://modernsproutplanter.com/how-it-works/ of a product that uses the method.
If you were to use the same type of small air pump, could the water be moved to a higher point?
Say I wanted to move water using this method, with a similar air pump, could the water be pushed up 600mm in a tube?

 

[A.T.]

If you were to use the same type of small air pump, could the water be moved to a higher point?

Isn't that what happens in your example?