A compressor is a device that reduces the dynamic range of an audio signal. First a threshold is established. When the audio signal is louder than this threshold, its gain is reduced. The amount of gain reduction applied depends on the compression ratio setting. For example, with a 2:1 ratio, for every 2 decibels the input signal increases, the output is allowed to increase only 1 decibel. A variety of other parameters in the compressor will also affect its performance processing specific signals; attack time, release time and others are very important.
There are a variety of uses and applications for compressors, the most obvious one being to control the dynamic range of a live performance so that it will fit into the fairly narrow dynamic range of recorders, etc. Other applications include making a signal's average level higher, increasing the apparent sustain on a guitar, evening out a vocal or bass guitar performance, fattening up sounds, and on and on. The list of possibilities is extensive!
A limiter is a dynamics processor very similar to a compressor. In fact, many compressors are capable of acting as limiters when set up properly. The primary difference is the ratio used in reducing gain. In a limiter, this ratio is set up to be as close to infinity:1 as possible (no matter how much the input signal changes, the output level should remain pretty much constant). The idea is that a limiter establishes a maximum gain setting, and prevents signals from getting any louder than that setting.
Like compressors, limiters are used for a variety of applications. A few: Maximizing signal levels while preventing distortion when using digital recorders, preventing overload in a signal chain, setting a maximum volume level to protect users of in-ear monitors, protecting speakers and amplifiers from clipping, and so on. Any time you want to establish a maximum gain setting and prevent signals from passing it, a limiter is your tool of choice ;)