The Dursleys often spoke about Harry like this, as though he wasn't there - or rather, as though he was something very nasty that couldn't understand them, like a slug. (Harry Potter and the Sorcerer's Stone)
A slug is a creature like a snail but without a shell. It is wet and slimy and considered rather repulsive.
The author is expressing that the family find him repulsive, treat him like he is stupid, and wish he wasn't there. But, much like slugs in the garden, is something that they have to live with.