When carrying out certain illegal activities, you will receive marked bills. You can view how many marked bills you have on you by opening your inventory and looking under your cash. Marked bills can be stored in hotels and houses, and given to other players.
There are money laundering services in the city. If you manage to find a sketchy gentleman around the city you will be able to give him your marked bills to be laundered.
The time to laundry can vary, up to an hour and a half. Make sure you have time to wait before you begin laundering money.