An extremely large, unspecified number.
Squillion is a fun and exaggerated way to talk about a really big number.
Examples:
There are a squillion stars in the sky.
I have a squillion toys in my room.
She ate a squillion cookies at the party.
I have a squillion things to do today!
I told you a squillion times to clean your room.
I have a squillion friends who all want to come to my party.