To be able to say that to the lender, (i'll put my property up for collateral) you have to show the lender proof that you own that property, or that the seller owns what he is selling.
Property ownership is recorded in the district courthouse at the land records office. Every time a piece of real estate is purchased or sold, both parties fill out and sign a form. The sale, once recorded on file, becomes part of that property's "chain of title" - that being simply the "list" of property owners over time. This "list" is available to the public. The chain of title also includes any mortgages or liens on the property. Mortgages are attached to a property when a deed of trust is recorded with land records.
As part of the process, the title company will help you payoff your old mortgages through the closing process. Old mortgage payment funds are escrowed at the closing, and then paid on your behalf. That old mortgage is then 'released' and recorded in city hall as paid in full.
The title company takes care of any taxes and fees regarding the transaction, paying them on your behalf so you don't have to deal with it. They underwrite the lenders insurance policy, as required by the lender, and then facilitate the loan closing. A property owner may also purchase an owners title insurance policy, to protect their interest in title.
So a title company will quite possibly save you many headaches in the long run, and also keep you out of trouble with their expertise and guidance. You may be treading thin ice if you venture in to major real estate deals without the backup of a knowledgable and professional title company to help you through the process.