In lending, pre-approval has two meanings:
The first is that a lender, via public or proprietary information, feels that a potential borrower is completely credit worthy enough for a certain credit product, and approaches the potential customer with a guarantee that should they want that product, they would be guaranteed to get it. This rarely happens in the financial services industry, usually what happens is pre-qualification instead.
The second meaning has to do with mortgage lending. People interested in buying a house can often approach a lender, who will check their credit and verify their income, and then can guarantee they would be able to get a loan up to a certain amount. The people can then take a letter of pre approval from the lender, and when shopping for a home can have possibly an advantage over others because they can show the seller that they are guaranteed to be able to buy the house.