Casual and Hardcore are terms used for MMORPG players. Most players will be described as either one or the other, though some see there being a middle ground between them called "dedicated."
Casual[]
Casual is generally a term for players who play occasionally and like rulesets that make the game easier and more fun. They usually are the kind of people who are busy in real life, not heavily into gaming, or share an account with one or more people.
Blizzard has made some effort to accommodate casual gamers with features like rest bonus. Compared to many MMORPG games, World of Warcraft is very casual-friendly based on the vast amount of initial content and territory, as well as solo-friendly content. A common complaint among some casual players is the difficulty in getting high-end gear (without committing hardcore amounts of time) either by repeatedly raiding for random epic drops or attaining sufficient honor points in PvP to acquire competitive epic gear.
Hardcore[]
Hardcore is generally a term for players who play a lot (30+ hours a week), prefer challenging play (PvP or cutting edge PvE), and don't like rulesets that make the game easier.
Blizzard definitely has lots of content for group-oriented, hardcore players with their focus on large raid dungeons (20-, 25-, and 40-man) and battleground PvP for more solo-oriented hardcore players.
In August 2023, a new Hardcore server type was added to Classic servers in which characters cannot be resurrected by any means, making death permanent.