Bhakti yoga is classically defined as the path of devotion, and it's often referred to as the yoga of love. Bhakti is one of the three primary paths to enlightenment laid out by Krishna in the Bhagavad Gita (the two other paths being jnana, the path of knowledge, and karma, the path of action, often interpreted as service to others). David Frawley, the director of the American Institute of Vedic Studies, calls bhakti "the sweetest of the yoga approaches" in his book Yoga: The Greater Tradition. He describes the practice as one of concentrating one's mind, emotions, and senses on the Divine in order to merge into the reality of divine love.
Essentially, bhakti yoga is the cultivation of unconditional spiritual love. Traditionally it involves devotion to a guru or a deity or deities, though Frawley points out that yoga teaches that there are infinite forms of the Divine: "Yoga gives us the freedom to worship the Divine in whatever form we like, or as formless." Whether you direct your love and devotion to a god, a guru, or the Divine in all things, as you cultivate a sense of love, gratitude, and devotion for something seemingly outside yourself, you essentially fill yourself with love. In the act of giving love, you receive it. The bhakti remedy for when you're suffering a broken heart, in other words, is to fill in the cracks with a love that is more permanent and transcendent. Practice long enough, and the subject-object love relationship (whether with a guru, a deity, or the Divine in some other form) disappears, and you become completely immersed in the love you are giving and receiving.