The human subtle energy system has been known and studied in the Asian cultures for thousands of years. It wasn't until the 1800's that Europeans and Americans began to be exposed to this information.
As William Collinge explains in his book, "Subtle Energy : Awakening to the Unseen Forces in Our Lives
", Einstein helped all of us to understand that everything, including human beings, is made up of energy. The cells in our bodies are electrochemical factories and processing plants. And beyond this, other types of energy that have not been detected by Western scientists flow in and out of our bodies and our awareness.
The simplest explanation that I have read of how humans interact energetically is in Sanaya Roman's book "Personal Power Through Awareness: A Guidebook for Sensitive People (Earth)
". Here, she explains that we humans are like radio broadcast towers, sending and receiving energetic vibrations all the time. We are constantly interacting on an energetic level.
We experience this energetic exchange as "getting the creeps" standing next to someone, or feeling the "vibe" of a party or a meeting long before you even see someone's face. We also have the very common ability to know when someone is looking at us when we have our backs turned away from them. This information does not come from our 5 senses, there is another type of sensing at play.
As a quick summary, the human energy system is made up of an aura, layers of energy bodies, chakras, meridians, and other various flows or pathways of energy. The following pictures illustrate the 7 main chakras and our layered aura respectively:

Chakras are whirling vortexes of energy and our aura is a layered cloud of energy that surrounds our body. Each layer of the aura corresponds to a chakra. The chakras and aura layers have specific meanings and associations. Check the individual pages for more detail.
When developing spiritually, meditating, and healing we are interacting with and affecting our subtle energy systems. Everybody has chakras and an aura which surrounds us like a cocoon. And all of the elements of our subtle energy systems interact with one another.
Our energy is always in flux, moving and shifting, changing colors (vibrations) and shape as we respond to people and everything else in our environment. By becoming aware of our energy we can begin to maintain it and support it for greater health and to take more control over our experiences in life.
Amazing things can be done while working with your energy. You can change your mood, protect yourself from others, discover information about what's bothering you, heal physical/emotional/psychological problems. The list goes on and on. And the work can be powerful!