Underwriting is part of the mortgage process. The underwriter is the person that looks at the amount of risk involved in issuing the mortgage to the buyer. They take into account all the factors of the buyer as well as the various factors involved with the home itself (via the appraisal). They typically will analyze your credit report, your income statements, and the appraisal of the home. Their determination results in an approval of the loan, or the disapproval of the loan.
Underwriters can be asked to re-evaluate the file if something is amiss. This process can add a few days of delay to the closing date though.