When you apply for any loan with a bank, the bank checks your income, purpose of the loan, etc. Based on these factors, the bank can tell how likely you are to repay your loan faithfully, and then decides whether to grant the loan and the other terms associated with it - like interest rate, duration, etc. This evaluation is called Underwriting.
Similarly, in insurance, underwriting is the process by which the insurer evaluates the risk & other factors associated with granting a life cover to the policyholder. For eg., age, health status, nature of work, location, etc. This helps the insurer in deciding whether to issue a policy along with other factors, like the policy premium.