The Origins of Yoga can be traced back 4,000 years to the Vedic shastras, which are the oldest and most sacred of Hindu texts. Hindu philosophy is based upon six principles, and Yoga is one of them. There are actually many types of Yoga found in the sacred Hindu texts, each with its own meaning. An example of some are:

Bhakti Yoga "Path of Devotion"
Karma Yoga "Path of Selfless Work"
Gnyana Yoga "Path of Self-Inquiry"

Bhakti Yoga was considered the path of devotion, because those that practiced it were most likely to view their deity with passion, love and worship. This type of spirituality is most similar to the devotion and worship that Christianity links with God. Although there are many types of Yoga, the type most familiar to Western culture is Hatha Yoga. This type of yoga focuses on controlled postures and breathing.

Hatha Yoga was brought to the Western world as early as the 19th and 20th centuries by Swami Vivekananda and Paramhansa Yogananda. Hatha Yoga found followers in western citizens who were mainly interested in a way to excercise both their mind and body. Yoga drew many practicers with it's focus on tranquility and balance. It's unclear exactly why Yoga has gained so many new practitioners and teachers during the early 21st century, as no one can really pinpoint when it became so popular.

I was unable to find exactly what made Yoga so popular, but I have my own guess, which I make no assumption as correct:

Yoga most likely had a slow and steady following since the beginning, but Madonna's public declaration of Yoga and Pilates' benefits may have helped bring it to the public. I remember Yoga being something I mostly didn't understand when I first heard of it, and then just slowly becoming something that almost every celebrity participated in. I think it's the key high profile yogis that have helped spread the word on Yoga. Also, in a world reliant and fully involved in the internet, the spread of information cannot be helped.