Mp3 is the most popular and widespread audio format. It was created by MPEG team in the 90s of the last century. MP3 format provides the quality of sound reproduction, similar to the original sound. The MP3 format is based on a lossless compression algorithm made to reduce the data size. In other words, music streams are compressed and deleted in the format that are somehow similar for listening on devices of common use.
The OGG format is an open and free standard with no patent and license restrictions. Nowadays, there is no clear standard for this format. Also you should understand that OGG is just a container for video and sound, and may contain streams encoded by different audio and video codecs.