When Input+ > Input- the output is high.
When Input- > Input+ the output is low.
Important specifications when choosing a comparator
Differential input – just like op-amps don't assume a comparator will operate rail to rail on its inputs, always look for the "differential input", "common-mode input voltage range" or similar rating to see over what range it will accept input voltages.
Standard Comparator Devices
MCP6546U (open drain output, rail to rail)
LM311 (open drain output, not rail to rail inputs: ground to VCC – 1.5 V differential input)