A lap dance is an erotic dance, usually performed for one sitting customer in a (strip) club. Sometimes physical contact is prohibited, sometimes (partly) admitted, probably for cash. The 'character dancer' is usually scarce (sometimes not) dressed.

The dancer is - usually for a fee - sometimes literally 'dancing' in the lap of the customer. What is possible and permissible between the two parties usually depends on the local laws and customs. And the price is negotiated between both parties. This ranges from aloof to extremely stimulating...

The origin would be in strip clubs where the strippers also received proffered money from customers. In 1980, Mitchell Brothers O'Farrell Theatre in San Francisco allowed that stripper for $ 1 tip naked sat down on the lap of a customer. Apparently, to the satisfaction of all parties. Customers (men, well..) flocked and use was quickly adopted by other clubs. Probably worked inaction on the nerves... and evolved shuffling and wobbling to the lap dance that we know today. Probably for $ 1 extra.

(not to be confused with tap dance;))

Tina Turner sings about it: I'm a private dancer, dancing for money...

"The only way to escape the temptation is to succumb.” Oscar Wilde