When Grand Theft Auto III was released by Rockstar Games and developer DMA Design (later known as Rockstar North) it changed the way games were thought about forever. The "open world" genre effectively started with the PS2 title and its October 2001 debut sold millions of copies, helped make the PS2 the "winner" in last generation's console wars.
The graphics (based on Criterion Games's RenderWare engine) and visual look were a bit simplistic and even a little cartoony in style but it also gave the designers a way to create a vast game world without having to worry about doing highly detailed visuals. Grand Theft Auto III and its two follow ups, Grand Theft Auto: Vice City (2002) and Grand Theft Auto: San Andreas (2004) improved the graphical looks slightly but all three games were built with the PS2 in mind which has relatively low hardware specs. Thus it wasn't hard to port all three games to the PC platform where one can expect users to have rigs that are much higher than the PS2's specs (all three games were released for the PC around six months or so after their debut on the PS2).