Compost tea is basically just as it sounds, a tea made of compost, and is generally used as a supplement to your
nutrient solution. It can be made of a "HUGE" variety of, and combination of different things. Thus how good it is, is really up to who made it. But generally you take good quality compost, beneficial acids, beneficial microbes, and brew then together into a liquid. You can either make a large teabag, or strain out the solids later. The main difference between the way regular tea is made, and compost tea is made, is the water temp. The water temp should be about room temp, hot water will kill the beneficial microbes. But another difference is the use of a large blubber in the bottom of the brewer. This helps keep the the brew churning, as well as promotes the growth of the beneficial microbes. Compost tea can be a good additive to use with your
nutrients, though I wouldn't consider it a replacement for hydroponic nutrients. Though some people do make their own, and use only the compost tea as their nutrients.
Here's an article about compost tea, and how it's made:
Organic Compost Tea for your hydroponic system
P.S.
I do understand wanting to support your local hydroponic supply store (any store). But I never willingly pay for anything when they say it's on back-order (unless I cant get it anywhere else). Simply because when something is on back-order there is never any guarantee when you will receive the product. You could wind up waiting weeks or even months before the product comes in. Meanwhile they hold your money hostage, and you usually cant cancel the order. So if you get the product from another source, your stuck with two of them. It may be a nice gesture, but compost tea dosen't cost them much to make. They should have given you some of another brand of "actual nutrients" they had on hand to get you by instead (in my opinion).