The rim is named CXP21. It's a semi-aero profile OEM rim, no eyelets, not bad, not great. Standard narrow profile (probably just under 20mm wide at the outside). Narrow road rims will take wider tires just fine, although there's a higher risk of pinch flats running a fat tire on a narrow rim. Hasn't stopped most mountain bikers though.
If you were building a bike from the start, choose wider rims (e.g., Sun CR18) for use with wider tires. However, as things stand, you'll be fine using tires at least up to 32c on these rims.
As noted above, the main issue will be the clearance on your frame and under your brakes. My good road bike can't fit 28c and above. This is the case with a lot of road bikes. Mostly stupid design.