The name Alloy rims simply means that they are not made of steel but of a mix containing (except some exotic ones) Magnesium or Aluminum.
The down side to them is mostly the price as they are made of more expensive materials and by a more expensive method (not just bent metal like normal ones..). Another down side is that they are strong but brittle – and so repairing them is unlikely and a strong curb hit will break them and not just bent them.
The up side is divided into several things, from the lease important to the most –
They look good – the metal finish is a sight for sore eyes, some because people like shiny things and some because the other advantages make it common in high speed, high power sport cars so we connect it (Alloy rims) to high speed and power.
The material has better heat conduction, which can help dissipate heat from the brakes which improves braking performance in more demanding driving conditions and reduces the chance of brake failure due to overheating.
Reduces the weight of the car as the material is lighter then steel and sometimes the rim needs less materiel as it has better mechanical properties (stronger).
And for the same reason it reduces the unsprung weight (weight that is not carried on the springs and shocks), now this is a major aspect as it greatly affect the grip – picture a car with no suspension at all (all it’s weight is unsprung) and I am sure you will agree that it bounces all over the place causing the tires to lose surface contact and grip. The less unsprung weight we have the better the suspension can follow the terrain. Check out this nice clip for some more info on this Unsprung weight