The electro acoustic guitar amplifier is designed to reproduce the natural sound of your guitar. You can get anything from a small 10 watt practice amp, such as the Ibanez IBZ10A, to a much more powerful amp with many more features including digital effects, such as the Marshall AS100D.
The bigger amplifiers may also have extra channels to allow the connection of microphones and an input that will allow you to play backing tracks; a feature which is ideal for the solo performer. It is also possible to use an electric guitar amplifier with an electro acoustic, although it will not reproduce that great natural tone of the instrument.