Chad Hurley, Steve Chen, and Jawed Karim, the Youtube founders, had all been former PayPal employees.
YouTube started as a platform for sharing videos for dating purposes. They wanted to share a video, but they couldn't find an appropriate place for it on the Internet. A dating YouTube wasn't popular. People started uploading amateur videos about other stuff, not related to dating.
The founders listened to their users and transformed YouTube into the all-kind free, video-sharing platform where each video had its own unique link. Back then, online video was quite buggy. Youtube solved this problem by introducing a flash-based, one-click videos.
YouTube got their first users by piggybacking on Myspace. Musicians on Myspace (the main Myspace's user base) wanted to show their music videos. YouTube provided a solution to that.