A minimum contract pays a player the lowest salary the league allows. A veteran minimum is the same idea for an experienced player, and teams can sign minimum deals even when they are over the cap.
In HoopSim the league minimum is $1.27M by default. A minimum offer is always allowed, whatever your tier, and it can even take you past the hard cap while you have fewer than 15 players. Free agents asking for the minimum are tagged Min on the free-agent page and sign on the spot, even during the season. You can offer a minimum deal to anyone else too; they do not have to take it, but the longer a free agent sits unsigned, the more likely they are to accept, and a better offer from another team still wins. When free agency closes, unsigned players are placed on one-year minimum deals with the thinnest rosters.
Rulebook: Minimum-contract players. Related: unrestricted free agent, hard cap.