The Sperm Bank allows characters to contribute sperm to it, so that other players may use it for their own purposes (Mostly for impregnating themselves).
Any character that produces potent sperm will be able to deposit sperm into the bank. Open the sperm bank on the website or using the HUD menu and click "Deposit". As long as you're at 100% potency, your sperm will be deposited into the bank. If you haven't reached your 50 deposit quota, you will also be compensated with 50SexP. Your deposit will last 30 days, and will be mixed with others of the same species if there are any. Each donor has an equal chance to be a father regardless of the amount they deposited, all that matters is that their deposit does not expire. Each deposit will only contribute 5ml regardless of how much the donor is able to produce normally.
If a female character becomes pregnant from the sperm, the father will be anonymous unless the mother or children uses a paternity test.
To purchase sperm from the bank, open the Sperm Bank tab and click the needle icon next to the species' sperm you wish to buy. You will be presented with a list of organs that you can inseminate. Each time only 5ml is used. Each deposit will be a mix of all of the donors of the same species. So there is always a chance that a resulting pregnancy could have different fathers.