These points are only accrued upon fulfilling one of your Sim's whims, or upon completion of your Sim's Aspirations (more that later, too). Satisfaction Points are The Sims 4's new version of Reward Points (introduced in The Sims 2). Much like Sims 3, however, when you successfully achieve your Sim's whim, you're rewarded with Satisfaction Points. Whims are a bit different from the wants in Sims 3 there are only three whims at a time, you can only 'promise' or save one whim at a time, and the whim on the far left constantly fluctuates depending on your Sim's mood at the time.
The Sims 3 had 'wishes' and The Sims 2 had 'wants/fears', but The Sims 4 has 'whims.' Whims are little bubbles that appear over your Sim's head in the UI, and they represent things your Sim wants to either obtain or achieve. Speaking of whims-they're technically new to the game, too.
