The study of the chakras is one of the most arcane and least practiced parts of yoga. The chakras are referenced in hatha yoga, sometimes in a classical sense, sometimes in a more 'new age' understanding – and I do not say that in scorn, as yoga is something as a whole that each age, and every person reinterprets for its own needs. Sometimes they are used with less precision, as in “open your heart chakra” is used to mean “all we need is love”. They can be understood as a conceptual paradigm, or as literal truth, as what Feurstein called “psychoenergetic centers”. To study them deeply in the second case can be done through the practice of Layayoga, which comes under the umbrella of Kundalini yoga.... which at least by my reading is connected more broadly with the practice of Tantra. For those who have not studied it I have a good idea what comes to mind when you hear 'tantra', and yes, that is there, but again, it is like understanding yoga as stretching on a rubber mat. Sure, ok, but not the whole story.
I think some context is helpful.
Do you remember in the movie “The Wizard of Oz” when Dorothy is wondering which way to take the road? (In the original series of books about Oz by Baum the questing metaphor is even more apparent). Well, that is kind of like yoga. Standing in a woods, and making a decision about which road to take. Yoga is a process of understanding, or spiritual quest. Hatha yoga, or the yoga of the body, is one path. When one practices it one seeks wisdom and self understanding, and spiritual understanding through the physical practices of asana, and pranayama, and so on. But those exercises are not not by themselves fully yoga.... there is also what brought us to do them. That drive to understand can send someone on a path of Hatha, but it could send someone else on a path of Karma yoga. In Karma we seek our way through service (every time you give someone directions, or pick up trash from the park, or make sandwiches for the food pantry you are engaged in acts of Karma yoga). And they are not mutually exclusive. One can walk different paths, and I think should do so, because humans are multidimensional beings. But often one path more than another calls us. I have always had a strong bent to Jnana yoga, or intellectual study. But if you only study, you risk not knowing fully your physical part, if you only exercise you risk being so self absorbed that your social self atrophies, if you only do good works your body could fail, and you might not know (by using your knowledge) what good works are best worth your effort.
One thing we have to keep in mind is that the attitude to the body has changed a great deal over the course of the history of yoga. Today we would most often view the body as good, physical health as important. But there have been in most cultures movements that have seen the physical body as something to be overcome, mortified, something subservient to the spirit. For some who practice meditation it is with the view of liberation from the physical. This is not just in yoga. Read the works of someone like Bernard of Clairvaux and you see this idea of the body as an obstacle to enlightenment. I think most of us view the physical more as a partner to spiritual development.
So the think about Tantra is that the body is taken to be a path, rather than an obstacle. And the thing about the chakras is that they are conduits spiritual energy.... doors between the spirit and matter, each door, like those paths through the woods opening at a different point, and channelling in different ways, if you will.
I am not a student of kundalini, or of the chakras. I do not practice Layayoga. I am more in the school of 'this is a conceptual paradigm'. But I think there is something in most people that we like to organize and sort, and doing so helps us understand things better. Like someone who had kids my kids used to play with whose play room had a whole wall of shelves, with different toys in beautifully labelled plastic boxes. The cosmos is constantly shifting chaos and order, and we are always trying to find the ways to put the puzzle together. I think even if you do not believe in the actual reality of the chakras, and the realm of subtle energy, or the auras, we can learn from them. After all a good poem may not be literal reality, but what it teaches us is often a deeper truth.
Having spent most of the time on context (rather my metier I guess) I will give you the 5 minute introduction:
There are 7 chakras. They are conduits for the 7 layers of energy that surrounds us. This halo, or aura surrounds and protects us. (chakra yoga is in some ways one of the most spiritual practices of yoga, and inherent in its practice is the notion of union with the divine by climbing the ladder of the chakras, at least in my understanding). Is the chakra in the body? Yes, but not part of the material body, but as part of a body form subtle in nature. The 7 are: The root chakra, the sacral chakra, the solar plexus chakra, the heart chakra, the throat chakra, the brow chakra, and the crown chakra.
The root chakra is about birth, connection to the land, and so on. The sacral chakra about our physical presence and emotional feeling. The solar plexus is about ego and action, the heart chakra about love, giving.... also about love moving past connection to one, to connection to the community of humanity (and forward to love for all, and for the divine). The throat chakra is about communication, about speaking, or presenting in truth, the brow chakra about wisdom and intuition, and the crown chakra about connection to the whole, about bliss, grace, however you want to put it.
Or as in the chakra meditation I shared on my Facebook page (and I am not sure who first came up with this, but it is widely shared in the community, and I think really brilliant):