5G is the fifth generation (the 'G' stands for Generation) of mobile data network. This is the way that data (rather than voice) is transmitted between mobile devices.
It will allow for even faster data transfer (think of really fast downloads and high-quality video streaming) and better support more devices in a small area (Useful for very crowded areas and IoT devices.)
For reference, previous generations are:
4G - The highest version currently in widespread use. Also known as 'LTE' which stood for Long Term Evolution. (You may see this represented as an '4'.)
3.5G - Slightly faster than 3G. Also known as High-Speed Data packet Access or HSDPA. (You may see this represented as an 'H'.)
3G - The third generation brought speeds fast enough to support video calls and streaming to a wide audience. (You may see this represented as an '3'.)
2.5G - Slightly faster than 2G. Also known as Edge. (You may see this represented as an 'E'.)
2G - The first popular technology for data transfer. (You may see this represented as a 'G'.)