Yoga is one of my favorite forms of exercise. It doesn't require running or any excessive activity, it's fun, pace can be easily adjusted and you still get results over time, and it can be done (almost) anywhere. I'm not saying you should stop and get into tree pose in the middle of the grocery store, but if you want to, go right ahead.
Yoga has been around for thousands of years, and it's not going to disappear anytime soon. It's more than just standing or sitting on a mat and getting into weird positions that look impossible to do. The reason yoga is different from other forms of fitness is because it focuses on internal and external activity. You focus on your breath while doing the action, and engage certain muscles that are required for the pose. It seems like a lot going on at one time, but that's the point. You're supposed to become aware of what you're doing at all times. That is one of the benefits of yoga is increased self awareness/self study. You notice patterns or rhythms that happen in and out of your body.
Yoga also helps with stress relief. Depending on your level (beginner, intermediate, advanced) and preferences, you generally start out slow, and end slow. That helps you get into the rhythm of the class or practice. The deep breathing exercises help you and calm you down. The deep breathing parts can be taken into a class or work environment to help with stress relief. Even though we may think that "taking a deep breath" doesn't help, it can really make a difference.
Strength building and increased flexibility are key components of yoga. This type of fitness builds muscle. You use many muscles in the body. Depending on the posture, you might use every muscle. Engaging these muscles helps build strength in them and overall. Not everyone can do a hand stand right away, but through continued practice of yoga, the strength to do it can be built up. Different postures require different levels of flexibility. The different stretches can increase flexibility in certain areas of the body. Over time, the muscles, tendons, and ligaments that get used will lengthen. Thus, creating more flexibility.
Yoga really helps you focus on the present. This is one thing that is hard for me since I always have something going on in my mind at one time. You have to focus on what you're doing at that time, how you're breathing, and how you're getting into a posture. This can help when you have to focus on other tasks that are in the present when outside of a yoga class. It helps with mental coordination, concentration, and memory.
Yoga has many benefits, and these are some of the many. Some have the misconception that you have to be flexible to do yoga. You don't have to be already flexible. That is something that gets worked on during class. Anyone can do yoga. It doesn't matter your age, strength, or energy levels. Yoga can be daunting at first, but that's why you start with beginners level (videos or classes) first. It is the one type of exercise that helps you in all of the different areas of life and body. Namaste.