In that weird era, (a) average home Internet connections became fast enough to support streaming video (with a healthy adoption growth rate), (b) the most widely deployed home recording device was likely still the VCR (digitizing analog video from cable to burn to DVD was a pain), (c) there was no "on demand" anything, as most media flowed over centrally-programmed cable or broadcast subscriptions, and (d) people capturing video on mobile devices was rare (first gen iPhone couldn't) but obviously a future growth area.
So early YouTube was literally unlike anything that came before -- watch a thing you want, whenever you want.