EDGE is an abbreviation for Enhanced Data rates for GSM Evolution. All network providers and smartphones support EDGE, but rarely actually make use of it. It's an ancient technology which came before 3G, 4G, and LTE, and is usually classified as a 2.75G network.
It was an evolution to GPRS and could achieve theoretical speeds between 120Kbps to 384Kbps. If you ever see an E icon in your smartphone's status bar, it means that your device is only able to connect to your carrier's EDGE network, which is due to you being in a poor network coverage area.
Even though EDGE services were considered super fast when they started to become operational back in 2003, you'll barely be able to browse through the internet with those kind of speeds nowadays.