The liquid that comes out of the bottom of your composter is more properly called "compost leachate". It may be nutrient rich, but may also be loaded with whatever pathogens were present in the feedstock. Use with care (probably not on edibles).
"Compost tea" is the product created by soaking finished compost in water for a period of time. There are various levels of sophistication that you can apply to achieve various levels of quality and benefits from your tea.
Teas contain nutrients, microbes, and fungi. The benefit of nutrient content is that it provides a liquid plant food with quickly soluble nutrients. The benefit of the microbes and fungi is that they may suppress some plant diseases when applied as a foliar feed (i.e. sprayed on the leaves).
Unfortunately "microbes" includes both beneficials and pathogens (like E. Coli). There is some controversy in the organic growing community about whether compost tea should be regulated like manure tea (which is regulated in the U.S. under the NOP). The science here is young and still trying to catch up.
The method and recipe used to brew the tea determine what it has in terms of nutrients microbes and fungi (aerated vs nonaerated, which "foods" were added to the brew -- sugars, seaweed, acids, salts, etc). Adding sugars will feed the microbes. Other ingredients will encourage fungi. Aeration will encourage certain microbes and fungi. Length of brew has an impact. Nonaerated compost that is brewed for a longer period will contain mostly anaerobic microbes since the aerobic microbes and fungi will have used up all the air in the liquid during the early part of the brew cycle.
The feedstock you use will have a huge impact on the effectiveness. If you start with weak compost you'll end up with weak tea. There's a lot of junk on the internet (especially where people are trying to sell you a system) that claims that compost tea has some kind of "magical" properties. But you basically get out what you put in.
If you're doing further research on compost tea, be careful which sources you choose to read. Most people selling "compost tea systems" seem to overstate the benefits (as expected). The scientific journals can be a little heavy to read. The University Extension services are pretty good sources, though they tend to oversimplify too often for my liking. This article at MOFGA is good, but is starting to be a bit dated. ATTRA tends to have accessible but comprehensive coverage of topics like compost tea.