This is an expression that you use to emphasize how little of something that there is. For example:
I'm not even supposed to be talking to you, much less helping you.
This means that the speaker shouldn't talk to the listener. Helping the listener is even less acceptable than talking to her.
The town I grew up in doesn't even have a grocery store, much less a shopping mall.
If the town is so small that it doesn't have a grocery store, it's certainly not possible for it to have a shopping mall.