T+1, T+2 and T+3, as well as other 'T+' numbers, refers to the number of days it takes to settle a financial transaction.
Funds settlement refers to the transfer of funds from buyer to seller and the transfer of title to an asset from seller to buyer. For most securities and trades, this occurs the same business day the trade occurs (this is called 'T+0'), although not long ago it took one to three days (referred to as 'T+3').
For example, when an investor sends an order to his or her broker and the trade is made with another broker/dealer or specialist, that trade information is sent to a clearinghouse such as the National Securities Clearing Corporation, which is a subsidiary of the Depository Trust & Clearing Corporation. This may settle in a day, or T+1. Similarly, a person who writes a check may see settlement in T+2 or T+0, depending on the nature of the transaction.
T+ funds settlement is an important 'back-office' function, and the faster it occurs, the more it reduces market risk by ensuring that trades are executed properly. Fast funds settlement also increases investor confidence in the markets by ensuring that their trades are completed on time and that they won't lose their funds to bankrupt brokerage firms or intermediaries. It also requires participants to have the money in their accounts as their trades are made (or arrange for credit before the trade is placed).