As metro said story progression happens in the background all the time. I take it you've played sims 2? Sounds a bit like it. So, assuming you have then sims 3 and story progression are completely different than the sims 2 way. So, as an example, you are playing the Landgraab family for a while. Then you decide to switch families, and go off and play the Alto's for a while. Then you decide to switch back to the Laandgrabs. But when you switch back to the Laandgrabs you realise that, whilst playing the Alto's, they've had a baby, changed career, or even moved house. That is story progression, because, whilst you were playing the Alto's story progression was making changes to the Laandgrabs. Story progression is responsible for keeping the town alive by making the residents have babies, or moving new families in.
Personally I adore story progression, I just love to see what is going to happen next. And it also makes no two game the same. For example, you create a family and play them in SV, keeping an eye on what happens to the Wolf family. This can be done through reading the paper and talking/visiting the family. So, i one game Thornton and Morgana Wolf have 3 children. You can then start a whole new game, play the same created family, but in this game Thornton and Morgana Wolf have separated, or Thornton is having an affair with Vita Alto! So, no two games are the same, no matter how hard you try.