A sim day is one day of the league calendar; to advance (or "sim to the next day") is to play every game scheduled on that day and move the calendar forward. In a sim league the whole league advances together.
In HoopSim a multiplayer league's clock moves only when it is advanced. The commissioner advances by a number of days, and every game on those days is played, with injuries, development, free-agent decisions, media stories and your inbox following. Per-game lineups and game plans you set ahead are used whenever the day sims. On sim nights everyone is taken into a live room where the games air quarter by quarter on the same clock. In a solo league there is no shared clock: you press SIM to the next game, to the next event that needs a decision (an option, an offer, your draft pick) or up to 14 days at a time.
Rulebook: How the league advances. Related: auto-advance, commissioner.