The center bore is the big hole in the very center of the wheel. It fits over the hub, which is the part that sticks out and centers the wheel.
If you get a rim with a bigger center bore, you lose the centering ability of the hub. As a result, the rims are very susceptible to vibrations because they are slightly off-center. I know some people who have lucked out and didn't have vibrations, but I also know plenty more who did all the right things when mounting their wheels, and still ended up with vibrations.
To avoid problems with vibrations, you can also get what are called "hub-centric rings", which are rings that mount on the wheel to reduce the diameter to that of the hub, but they have some problems too (especially plastic ones, which can deform or melt).
One more certain way to avoid the vibrations is by getting what are called "wheel adapters", which mount onto the stock studs and come with their own separate set of studs. However, they change the suspension geometry by pushing the wheels out beyond the stock position, so they're not necessarily desirable either.
Those approaches fall under the general rule of "it's not a good idea to change something in a way that's just going to cause additional problems that require more changes".
The easiest way of avoiding these problems is by sticking with wheels that have the same size center bore as the stock wheel setup.
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