The power goes from hot (breaker) --> switch (wire should be black) --> [when switch is on] lights (wire usually red or another color).
Check voltage at the black wire at the switch. (Should read ~120AC between that wire and ground). If you're not getting voltage at the incoming switch wire (black), the problem is upstream to the switch. Did you check the breaker? (in your service panel, usually in basement, is one of your breakers tripped / showing red)? If the breaker is not tripped, then there's a break in the wire connection between the breaker and the light switch. Is it possible the switch is downstream from a GCFI outlet, which may be tripped? Check all your GCFI outlets...
The two white wires together are neutral. The black is hot (from breaker). The red is switched (to lights). The black and white together are probably switched or hot on another circuit, but they are not applicable to the light circuit in question.