A right handed fishing reel is one in which you use your right hand to turn the handle. For left handed reels you use your left hand. Most spinning reels allow you to change the handle from left to right as you desire. Baitcasting reels have the handles on fixed sides and they can not be moved.
People tend to reel withtheirdominant hand but in the end it comes to personal preference andergonomics.
This MAY be a cultural thing (not sure) but many anglers (most, in the UK) will turn a reel handle with their non-dominant hand, holding the rod (and reel) in their stronger hand.
Consequently, a right-handed reel (as used by an angler with a dominant right hand) will have the handle on the left, and vice versa.