Would you care to (do something)?

This is a really polite, formal way to invite someone to do something. You use it like this:

Would you care to accompany me?

You can also ask with "for":

Would you care for a drink?

It's so polite that sometimes people use it with their friends as a joke. The joke is that you're speaking in a really formal way, even though it's not necessary.

join (someone) (somewhere)

This means to go somewhere where a person is going to be:

Will you be able to join us at the party?

Would you care to join me in the bedroom?

(do something) on the dance floor

A "dance floor" is an indoor area where people are dancing (or where they're supposed to dance).

When you're in a situation where there's dancing going on, you can talk about the things that are happening "on the dance floor". Here are some things that people do on the dance floor:

• get out on the dance floor (start dancing)
• get down on the dance floor (dance enthusiastically)
• go crazy on the dance floor (dance wildly)
• see someone on the dance floor