It means that no matter what you have in life, what someone else has always looks better.
Soo imagine a goat in a field – he has green grass all around him, but the goat in the other field seems to have lusher grass and so he will go over to the field to have what the other goat seems to have….but when he gets there he will realise it is not as he first thought and look back at his old field and think, ‘hey – the grass was greener over there – look at them all having a good time.’ and will want to go back.
Lets say you have a married man who looks at his single friends and thinks they have the better deal – so he leaves his wife to have the single life again, but then realises it is not all he thought it was, and he begins to miss the stability and comforts of home, and wants to go back…
Basically the saying is means that things might look good somewhere else but that is not necessarily true…because from the other side, what you have might look pretty good to them.
LOL the more I try to explain it the more confusing it seems to get! I shall stop now before I give everyone a headache!