The answer to this question depends on the object and its typical use. Floors, Countertops or Furniture are obviously used in a different way than walls or ceilings.
Walls, ceilings and decorative objects which are usually not regularly touched, are dry enough at the time listed as “touch-dry” – i.e. that’s when you can continue using a freshly painted room. Avoid producing dust, though, as some areas could still be sticky at that time.
Floors and countertops can be lightly used after 12-24 hours if they have been painted with water-based or latex paint. Light use means: you can put lightweight objects on it for a little while or walk on it, preferably with socks rather than shoes or slippers. For oil-based paints, wait at least 24 hours though.
A regular use, e.g. putting or storing heavyweight objects or furniture on a floor or cleaning / wiping a surface, should be possible after 3-7 days. However, wait longer if you can to be on the safe side.