Usually a squid is an overprotective boyfriend or clingy girlfriend.
It's based on a sailor being stolen from his ship by a giant squid and taken to the depth of the sea never to be seen again.
1. A synonym for alternateen from the mid to late '80s. A punker, skater, goth, etc.
2. A fan of New Wave music, as opposed to definition 1.
3. A look-a-like for Duckie from Pretty in Pink.