SDW - Rim type is usually irrelevant as long as it's the right diameter, in this case 700c. The second number refers to the mm width of the tire. Narrower tires are faster, fatter tires more grippy and shock absorbing.
You only need to worry about the clearances your frame offers, often higher end race frames have very tight frame clearances that will only allow a max tyre width of say 26-28mm. So, if there's plenty of room either side of your existing 23mm tires then you would be fine with these.
32mm is pretty fat though, more for a touring bike or hybrid.
SDW - Rim type is usually irrelevant as long as it's the right diameter, in this case 700c. The second number refers to the mm width of the tire. Narrower tires are faster, fatter tires more grippy and shock absorbing.
You only need to worry about the clearances your frame offers, often higher end race frames have very tight frame clearances that will only allow a max tyre width of say 26-28mm. So, if there's plenty of room either side of your existing 23mm tires then you would be fine with these.
32mm is pretty fat though, more for a touring bike or hybrid.
Hope that helps! :)