unless you play in an acoustic band, you're going to need monitors of some kind to hear yourself sing -- without them (and running properly) you can easily get off pitch and not know it.
Monitors come in all manner of configurations and quality. Easiest are "hot spots" which are little, self-powered small monitors that can be mounted on mic stands right near you. Next would be floor monitors that sit on the floor angled up at you (these are the typical monitors most traveling and pub bands still use because they are affordable). Then you have in-ear monitors, which are the "hearing aid" looking devices you see all major acts using -- they offer great control without any additional on-stage volume (as floor monitors will create), but they are expensive compared to hot spots or floor monitors.
With any monitor, you need to be able to send a signal to the monitor -- typically a "monitor send" from your main (or "front of house") mixing board. Google "stage monitors" and you'll get all the details you need.