When is a polar molecule?

Answer 1

when one part of it has a higher electron affinity that isn't canceled out by another.

example:

H2O

H-O-H

Oxygen has a very high electron affinity, it pulls on electrons a lot harder than other atoms (except fluorine, which has the highest electron affinity).

Oxygen pulls the electrons away from the hydrogen atoms giving it a relatively negative charge, and giving the hydrogen atoms a positive charge.

But:

CO2

O-C-O

Both Oxygen atoms are pulling on the electrons the same amount so there aren't any more in one part of the molecule than another.

That's the basic explanation.