Details like your airline/rail/bus bookings, hotel reservations, etc. are taken care of, so you can relax more.
A professional firm will be able to tell you which places to visit according to the time of the year (season), your budget.
If you're travelling abroad they can also take care of procuring your visa. Be sure to give them advance notice.
In choosing your travel agent:
Always depend on reputed names. Even if the prices are a little steep, you are in safe hands.
For instance:
An agent may show attractive brochures of five star hotels where you will stay, and on reaching the destination, may put you up in a three star. You end up paying more for less. To be on the safer side, ask the agent to produce confirmation of reservations in your name from the hotel.
Also check the menu the agent offers. You may have to put up with insufficient meals at the destination if you don't.
If an agent offers an attractive lower price for a round trip, check small details like sightseeing charges, etc. He may take you to places which demand expensive entry fees and you will have to cough up more money than expected. The transport for sightseeing may also not be of good quality. Try and crosscheck as many details as you can. Also compare one agency's rate with the best in the market and see what that agency has to offer.
Lastly, except for the business traveller, not many people have a passport ready. Instead of rushing it through in the last minute, apply for passport well in advance.