A single player game is one intended for a single user at a time, with no interactivity with other users. As I mentioned above, you can play a single user game on your favorite computing device with or without an Internet connection. Multiplayer games are typically played online (often with strangers on the Internet) but don’t have to be. For example, if your kids are playing Mario Kart on a Wii gaming console with a split television screen, that’s a multiplayer game independent of an online multiplayer environment. From the perspective of inappropriate contact with strangers, single player games are clearly safest, whether they’re online or standalone.
From a game play perspective, multiplayer games tend to be inherently more interesting for gamers, particularly when the nature of the game is inherently interactive. If the opponent in your game is simulated by the computer, it will fall short of feeling real. In contrast, if the opponent in your game is controlled by an actual player, the game play becomes significantly more rich.