There are actually several branches of yoga, including bhakti, the yoga of devotion, and jnana, the yoga of knowledge. The most widely practiced branch in the US, the one typically offered at gyms and exercise studios, is hatha yoga, which is physical yoga. But there also are different styles of hatha yoga, from the exercise-intense power yoga to the gentle chair poses used in svaroopa yoga.
Many of the instructors offer integral yoga, which involves stretching and bending into various positions called asanas, as well as breathing exercises and deep relaxation. By practicing and learning asanas, students can gain flexibility, strength, stamina and improved circulation.
Integral yoga is not religious, but it does offer an introspective, spiritual component that you won't find in most exercise programs.
A typical adult class lasts 1 hour. First, the students center themselves through breathing, then come together as a group with a collective om. They do a quick series of cardiovascular movements, an hour of stretching and 20 minutes of relaxation while lying on their backs.
The relaxation period gives students a chance to turn inward. Some people are making lists in their head. Some people are asleep. Some people are just in a really great space, where they're conscious of what's going on in the room, and yet at the same time, completely and unequivocally out.