A contact approach lets you proceed to an airport visually, more or less as if you were granted Special VFR, without having to cancel your IFR flight plan. This gives you the luxury, if you have to climb back into the clag for some reason, to proceed to fly the missed approach procedure and proceed to your alternate (or whatever ATC tells you to do), etc, without having to get a new IFR clearance, and in the event of a comm failure, you have a plan to follow and which ATC can anticipate (most IFR procedural requirements are to cater to the comm failure case).
Without the contact approach option, and you wanted to proceed visually for whatever reason, you would have to cancel IFR and proceed VFR, requesting special VFR if there is a control tower, and then if the weather closes in you have to remain VFR as best you can until you can call for a new clearance, which you would have to take down while clunking around at 1000 ft.