Bhakti is the yoga of love and devotion. It is the essence of devotion to a god.
Yoga means union—union with god. A yoga is a path to god (and physical, or hatha yoga, is only one, very preliminary type of yoga). There are endless types of “yoga,” especially in our modern, yoga-commercialized world. But to go to the root, it’s good to start with the classics: Swami Vivekananda, the first Hindu to bring the philosophy of classical Indian yoga to the West (at the 1893 Parliament of World Religions), defined the principle four types of Yoga thusly—karma yoga, or unity with god by work in the world (think Mother Theresa); jnana yoga, or unity with god by knowledge and study (think St. Thomas Aquinas); raja yoga (which is similar, though not completely identical, to what we commonly think of as kundalini yoga—think of the standard cave-dwelling Indian yogi); and, finally, bhakti yoga, or yoga by love and devotion.
The bhakti yogi, or bhakta, is one who fully opens their heart to the divine, and by constant prayer and vocalized praise, both spoken and musical, the bhakta slowly achieves union with the object of their devotion. In many ways, bhakti is the easiest yoga for Western people to understand, as Christianity is essentially a bhakta path. The Christian devotee who opens their heart to the love of Christ, and through fervent prayer achieves a kind of mystic communion with their ideal—this is bhakti yoga.
In India, the classical example is devotion to Krishna, through group song, chanting, prayer. But though the object of devotion may be different, because of the cultural gloss, the effect is the same—the opening of the heart to the divine.
Modern practitioners of bhakti yoga might gather in small groups at yoga studios to sing group hymns to the divine, participating in group song and leaving with uplifted hearts, minds and souls. Or they might be performing right in plain sight. Take this popular song from the late Beatle George Harrison:
My sweet lord
Hm, my lord
Hm, my lord
I really want to see you
Really want to be with you
Really want to see you lord
But it takes so long, my lord
I really want to know you
Really want to go with you
Really want to show you lord
That it wont take long, my lord (hallelujah)
(From “My Sweet Lord” by George Harrison from 1970, composed as a hymn to the Lord Krishna.)
This is one of the best modern, Western examples of bhakti (other uplifting, powerful Western masters of bhakti include Krishna Das and Wah!)—but no matter the time period or language the bhakta sings their song in, the basic message is the same: love for and devotion to God.