Steeping is how you make tea or herbal infusions (
http://coffeetea.about.com/cs/teabre...t_brewcup.htm). It's dunking your tea bag into hot water, or pouring hot water over loose leaves. You "steep" the tea in the hot water for a certain time (4-8 minutes depending on the type of tea), then you remove the tea leaves -- you take out the tea bag, or the tea ball, or you pour off the tea into a separate container leaving behind the loose leaves. Then you drink the resulting liquid. If you keep the tea leaves in the water too long, it gets strong and bitter and rather acidic.
There's a lot of paraphernalia that can be involved in tea drinking. But most Americans just stick with tea bags. Easy to use, no muss-no fuss. You don't need a pot, or a tea ball/infuser, or a strainer, or a cozy (a kind of "sweater" for your tea pot to help keep it hot) or anything. Just a cup/mug and a tea bag.
Some folks like to use "loose tea" which means it's not pre-packaged into bags. You can get a lot of varieties loose that you can't get in bags. You can put it in your own tea ball, or use a special tea pot with an infuser basket, or just use the tea loose in the pot as long as you plan to pour off the liquid when the steeping is done.
There's even a special kind of brewing done in China in very small tea pots. They look like they hold only enough for one cup of tea. But you use the tea over and over. You fill the little pot with tea leaves, and pour over your water. After it steeps, you pour it into your cup and drink. Then you put more water into the pot, with the same leaves. You steep, pour, and drink. Oolong tea, especially, is enjoyed this way, as each steeping results in a different strength and character of tea. When I lost 30 pounds, I bought a Yixing-style tea pot as my reward. It's the loveliest little thing. (
http://funalliance.com/tea/yixing_all.htm)
"Brewing" coffee is different, as it is often done over heat -- boiling the coffee with the water, or percolating it up and through the grounds. You can get "coffee bags" that you can steep in hot water like tea bags, but most people I've talked to think it makes really sucky coffee.