Yoga has its known roots in India, a hot and humid culture. Now the discipline with its focus on developing the person as a whole has developed into many branches with many different motives. The most traditional yoga lineages did not hold climate as an important factor for the practice but some modern teachers, Bikram Choudhury as an Indian pioneer of the heated form have chosen to replicate the culture and climate of India since these were the conditions in which yoga asanas, or poses, were created.
Heat allows practitioners to increase their flexibility and thus aid the body in moving with ease from one posture to another. It also helps hold a pose longer and go a little deeper when joints might be stiff from the cold.
There are advantages and disadvantages to every style of yoga, including the use of heat. If you are more flexible than normal in a class because of the heat you could push yourself too hard. Then again, if you struggle in this area the heat can help ease you into movements that will add to your overall conditioning in every day life.
Bikram yoga is practiced at 105 degrees. It is today the most popular style of hot yoga. Named after its founder, it utilizes the repetition of 26 poses that Bikram attributes to restoring his own health when he was a young man in his twenties.
There are other forms of hot yoga growing in popularity. Power Yoga (coming from Ashtange Vinyasa Yoga) also replicates another culture, that is Mysore. Forest Yoga is a combination of the asanas and native American spirituality, giving the practitioner a taste of a sweat lodge in the yoga session. Lastly, TriBalance Yoga utilizes heat but not humidity.
These are superficial overviews of the four popular forms giving you a sense of the purpose of hot yoga.