LTE stands for "Long Term Evolution" in terms of phones. It is often used to refer to mobile networks as phones display LTE when they are in LTE-serviced regions.
The Long Term Evolution serves as a standard for a transition into faster wireless data networks and an increase in capacities of these networks. LTE moves beyond 3G and allows for faster downloads on mobile and wireless devices. The need for LTE has arisen since so many more consumers have mobile devices than in years past and want to use these devices for things such as downloading and streaming music and HD video.