What is solo roleplaying?
Its playing a table top rpg by yourself. Often it is compared to a single player hexcrawl/dungeon crawl or creative journaling/writing. Although its not a 100% replacement for social role playing, it can be a great way to practice, get experience in systems or fill in if the gang can't get together for a game.
Here are some introductory Youtube Videos which I think explain it better than I ever could.
Geek Gamers' solo RPG tutorial playlist
A long running and amazing solo roleplaying/gaming channel.
A high quality actual play of solo roleplaying.
Mythic is the grandpa of modern solo roleplaying. It has its own built in system, but