Okay. You know what your loan officer does for you, what your mortgage processor's role in your loan transaction is, who will order the property appraisal and have a basic idea of what they look for and now on to the pesky title report.
This is very State specific so I will only give a brief overview of this step. If you have a relationship with a title/escrow company or an attorney who does this type of work you can certainly use them. Just let your mortgage processor know so they can check to make sure this company is approved with your lender. If you do not have a relationship established, in purchase transactions I typically advise that you use one of the companies that your Realtor recommends and in refinance transactions I typically advise going with one of the companies that your lender recommends.
The title company will order a courthouse search of the property and compile that information into a preliminary title report. This will include the current and previous owners, the legal description of the property, any easements or other issues as well as any liens against the property. Any liens must be cleared prior to or at closing. If you are purchasing the property, this is the seller's responsibility. If it is a property you own, you will need to take care of the liens.
Every lender requires title insurance and when you buy a home you also need it. This protects you from title defects (undisclosed liens, boundry disputes etc.) and it protects the lender's lien position.
The title/escrow company is also responsible for the actual loan closing, notorizing signatures on legal documents, recording of the mortgage and deed and dispursing any funds.