There are two things that “larger” may mean here. That inch size is the size of the rim. Many cars come with ghetto rims like 20 inch that have very low profile tyres on them so the outside diameter is about the same as the normal tyre would be. Tyres looking like this kind of tyre are often used when racing for addition road feel etc. The problem is first they tend to be easily damaged by that first pot hole and they are expensive, but not nearly as expensive as the real racing versions that are not that easily damaged. Most people would find the ride not as comfortable as the standard design.
The other type are larger tyres along with a higher suspension. Those wheel/tyre combination look more like truck tyres and are good for off roading. Most people buy them for looks. They will cost more and they will reduce your mileage some. They can make access to the passenger compartment more difficult. These tyres often have aggressive tread design and that makes more noise. That is the source of the road noise you have heard about. Getting tyres with less aggressive tread will take care of that.