Linear independence, spanning, and the three bears
Papa’s bed is too hard – linearly independent, but too spare to span.
Mama’s bed is too soft – spans, but too many options to suffocate in.
Baby’s bed is just right – enough to span and nothing more. A basis!

Coordinate vectors and sweets
A restaurant serves 2 desserts, cannoli and cookies. Bill and Bob walk in. Bill says, “I’ll take a cannoli and two cookies.” Bob says, “I’ll take 3 cannoli, no cookies for me.” Finally, Xavier walks into the restaurant and says, “Hmm, I’ll take 3 of what Bill’s having and 2 of what Bob’s having.” To figure how much to give Xavier, the server thinks “He needs 3*1 + 2*3 cannoli and 3*2 + 2*0 cookies.”

[of course the server really thinks “what is wrong with this guy?” but we’re in math fantasy land, so suspend your disbelief.]