Mortgage pre-approval establishes your buying power and strengthens your offer by telling the seller that you have already qualified for the loan and financing that will be written into the contract. In today's real estate market, very few sellers (if any) will even consider an offer that doesn't contain a clear and well-documented financial picture of the buyer.

Sometimes a buyer will realize he or she really wants to complete a purchase in a price range above the initial pre-approval.  Your mortgage lender can run all scenarios for you, and you can decide if you can access another source of funds or carry a higher payment.  It's impossible to emphasize how much stress will be reduced for you if you know all of your numbers before you write an offer and get into counter offers on a property you've fallen in love with. 

It's very common for buyers to finance with money from different sources - work income, savings, borrowing against investments, cashing out investments, gifts from relatives, and other real estate or real property that needs to be sold.  You may not want to cash out these assets until you've found the right house.  However, you need to know how each will be handled, what the tax implications are, and what timelines will be BEFORE you write an offer.