[1] For a general loan 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.
For a mortgage, people interested in buying a house can often approach a lender, who will check their credit history and verify their income, and then can provide assurances they would be able to get a loan up to a certain amount.
Buyers can ask for 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 more likely to be able to buy the house.
Often real estate agents prefer to work with a buyer who has a pre-approval as it demonstrates that they are well-qualified to receive financing and are serious about buying a home.
[5] This is disingenuous by the companies because they fully know that many consumers will see it and believe it means they have already passed the approval process when in fact they have not.