A hardtail mountain bike has no rear suspension unlike full suspension bikes. The advantages of this is a lighter bike, a great entry level mountain bike, a cheaper option, and its a very easy to maintain bicycle. It also encourages a good starting point for any new mountain bike in offering a solution to gain that much needed trail experience and riding styles.
Although full suspension bikes are what most people look for today you cannot argue with the precise handling a hardtail bike offers especially over heavy terrain. Many people now opt for a 29" wheel as they offer a smoother flow of ride over rough ground.