Technically speaking, all yoga styles come under the umbrella term of hatha. Hatha was the original yoga 'style' that incorporated yoga postures (or asanas). These days, the term hatha refers to a more traditional yoga style that's stayed close to its ancient roots.
Unlike vinyasa yoga, where postures quickly flow from one to the next, each posture is usually held for some time in hatha yoga. This might be 30 seconds or a few minutes depending on the class and level of the student. Long holds have many benefits; from stimulating the internal organs to giving the mind a chance to find much-needed stillness. In general, hatha classes tend to be slower and more relaxed than vigorous styles like vinyasa, Ashtanga, and Bikram.
Hatha yoga classes usually incorporate more than just the yoga postures. Breathwork (pranayama) is usually included, which calms the mind, grants energy, and develops focus. Meditation is often included as well, making hatha yoga classes very well-rounded.
Hatha yoga is a great place to start if you're a beginner. Because more time is spent in each posture, you'll be able to learn proper alignment and how to work with the breath. However, even if you're not a beginner hatha yoga is still a great choice. Classes are well-rounded and leave plenty of room for physical and mental challenges.
If you're stressed or feeling ungrounded, the slow pace of hatha will help bring your mind back to a balanced state. If you're easily bored, on the other hand, you might try a style with a faster pace like vinyasa.