How is the VA involved with home loans?

The VA does not loan money; they guarantee a portion of the loan to the lender loaning the money. Should a loan go into default, the VA guarantees an amount to the lender so there is less risk to the lender. Less risk equals better rates in most cases, which is why VA loans are becoming more popular with lenders and generally have lower rates than other types of financing.
The VA gives a base of guidelines, which the lender uses to qualify and underwrite the loan. However, lenders can impose overlays, which are additional requirements to approve the loan.  Since the lender is the one who is taking the risk by loaning the money, they must ensure the approval is for a qualified candidate. Click here for more info