It's all about making sure everybody knows what's going on. While you are on an instrument approach and thus flying IFR, ATC is responsible for spacing you, giving instructions on heading and speed in order to fit you in with other inbound aircraft. In that situation they expect you to confirm and follow those instructions, and if you don't it makes for a lot of headaches.
If you're on a visual approach, such as when you've cancelled your IFR flight plan after descending below sparse clouds with the runway now in plain sight, then the tower knows not to give you spacing instructions; they instead space IFR traffic around you, while other VFR traffic just has to maintain their separation minima from you. Knowing that you're on a visual approach means ATC won't waste their breath trying to get you to adjust your airspeed, altitude or course to follow a traffic pattern; they'll just give those instructions to other aircraft in the pattern to maintain a steady traffic flow.
... unless you're in Class B space. If you are flying into a Bravo airport, you can still request a visual approach, but approach control has to OK that change (especially for airliners), and ATC is still required to provide separation services to you whether you're VFR or IFR, so they can still give you instructions regarding your airspeed to make sure you fit into the IFR traffic pattern. This may, at times, require an uncomfortably fast landing for GA pilots being spaced in between commercial airliners at a busy time. Some Class Bs like Phoenix or DFW will have a runway more or less reserved for smaller aircraft so there's less disturbance to commercial airliners with higher approach speeds, but not all airports have that luxury; if you want to land your small single at O'Hare or Dulles, you'll probably find yourself spaced in-between airliners and forced to very precisely time your approach so you can touch down and clear the runway in time for the plane behind you to take off. If traffic is heavy, you may not get in if you greet them with "Hello O'Hare Approach, Piper 354 Alpha...". As soon as the O'Hare controllers hear your GA small-prop callsign, if the pattern's too busy they'll deny you Bravo entry and recommend you head for a smaller airport like Chicago Exec or Gary.