But what does this empowerment actually entail? That their Daemons grow in strength/number? That their ability to posses/enlist mortals increases? The minions of each Chaos God are focused specifically on inflicting/indulging in whatever strengthens their Chaos God, but to exactly what end? I'm not aware of this "strength" being a decisive factor for any battles/ect.
In the Warhammer 40K Universe, all of the Chaos dieties except for Slannesh were incredibly powerful long before Humanity made it into space. (See: Why is Slannesh so young when compared with the other Chaos Gods?)They received worship from thousands of worlds and because the base nature of these deities tied into emotional states of billions upon billions of souls living and dying, they attained a spiritual existence which then turned around and created representatives of themselves to the beings who were most able to promote conditions conducive to needs of the Power in question.
Think of each Power as a priesthood, where extraordinary representatives promote their Power gaining spiritual capabilities, battle rages, new diseases, new means of obfuscation. These new abilities lend themselves to create more of what the deity needs to survive. Like any other master/servant relationship, the deities keep more of the spiritual power they harvest from fallen souls than they share with their representatives, thus keeping their representatives seeking new powers and new sacrifices, while the deities miserly give out tools, resources, demons to their agents, as necessary.
These Powers are not above, however, disposing of Agents whose powers grow too large or who fail to tow the divine line possibly creating heresies or new religions, altogether. Most Agents of Powers, remain devoted as long as they are able to do what they want when they want. There are far too many tales among Chaos worshippers of Agents who decide they are smarter, more powerful or wiser than their Chaos masters. This rarely ends well for the former Agent.
In simplest terms, exposure. Take, for example, Khorne. People exposed to gratuitous slaughter tend to either withdraw into their own faith (space marines) or begin to break and go insane. When they've fallen into insanity, they essentially become more pawns for Khorne. The power of any diety is propotional to that of their followers beliefs. The Chaos Gods are a major force in the universe, because so many people believe in them and follow them. They would be greatly reduced in power if, as an example, every one of their followers left them behind. To prevent this, the chaos gods take steps to ensure the loyalty of their followers. Nurgle infects his with diseases and makes them strong, Khorne shatters their minds, etc etc. Both groups, the gods and their followers depend on each other.
If you've read the Soul Drinkers books, the story of Tellos is a wonderful analogy.
He and his marines were abandoned in a huge battle. They had already showed some slight blood-tendencies, and in order to survive, they gave themselves over to Khorne completely. Khorne gained powerful followers, while the marines gained great strength and survived. Both parties were strengthened by this, Khorne more so, because the devastation that his newest bezerkers wrought led even more people to his worship.
I have talked with friends and theory that has stuck with me was that all the humans are minorly psychic. Their combined fear has helped fuel the manifestations of the big 4. Fear of war, fear of mutation, fear of diseases, and fear of excess (or whatever else slanesh is). It is an interesting idea, but i am also aware of the Eldar creating slanesh. On a side note that friend also proposed that Horus is on the Golden throne and not the Emperor.
edit some more evidence of the major populations of people being psycers is that "blanks" (people who push back the warp) make normal people uncomfortable. That discomfort could be the result of the latent abilities of the general population.
The Chaos Gods were born from the raw emotion of mortal races being reflected in the warp:
In the warp, similar thoughts and emotions gather together like rivulets of water running down a cliff face. [...] and such is their power that they formed creatures made of the very stuff of unreality.
Eventually, these instinctual, formless beings gained a rudimentary intelligence. The Chaos Gods were born - vast psychic presences of the fantasies and horrors of mortals.
- Codex: Chaos Daemons, 6th edition, page 6
The Gods can only gain the power from the mortal realm and they can then use that power to empower their mortal followers:
A Chaos God can only grow in power through the actions and thoughts of mortals. Those who worship a Chaos God , and behave in a way that feeds it, are rewarded with strange gifts, extraordinary powers and, potentially, immortality.
- Codex: Chaos Daemons, 6th edition, page 6
The Gods can also use their power to create more lesser daemons:
A Daemon is 'born' when a Chaos God expends a portion of its power to create a separate being.
- Codex: Chaos Daemons, 6th edition, page 7