Compost tea is making a tea or infusion from your compost
There's a whole huge thread in the Compost Forum about ACT, sometimes called AACT (aerated, activated compost tea), you can read as much as you want to.
Done right it is a bit complicated, because of the aerated part... it needs a pump, airstone, timing the brew for 24 - 36 hours, and then sterilizing all the equipment afterwards. I haven't gotten in to doing all that (yet?), but I make a compost infusion, by putting a small shovel of compost in a bucket of water (rainwater or tap water that has sat over night to outgas the chlorine), add some molasses, and keep stirring it for awhile.
The molasses and compost gets the microbial activity started. By making it into an infusion, a little bit of compost goes a lot farther in your garden and you can use it for a foliar spray.
Whether buying or making compost, unlikely that you will have enough to use on the whole yard, probably best on the garden spot. But if you did happen to have enough, it would be fine for the whole yard. Compost is good for lawns too.
I do keep a compost pile all winter, to have something to do with my kitchen scraps. It mostly just sits there frozen, but starts working again in the spring ... it is already active and filled with earthworms!