Sourdough bread is bread that has been all or partially risen with the help of wild yeast. It is made sour because of wild lactobacilli that are picked up with the wild yeast. Where the yeast eat sugar and produce CO2 for rising- the bacteria create acid and other compounds that make the bread sour and distinctly flavored.
Because of the wild nature of the microbes, the bread will taste a little different in every place that it is made. The lactobacillus that gives San Fransisco sourdough bread its characteristic flavor is actually named Lactobacillus sanfranciscensis.
The starter can be a hassle to make and to keep. It requires almost daily attention to feed it and can waste a fair amount of flour unless you bake bread frequently. You can freeze the starter but it will require a few days of feeding before it can be used again. Many baked recipes besides bread are also delicious with sourdough starter. Sourdough waffles or coffeecake are fantastic.
Whether it is worth the effort is a personal decision. Many people don't like the flavor and you would have to love the flavor enough to make almost every bread with that flavor to justify the starter upkeep. Personally- I used to keep a starter but my kids don't like the flavor and I got tired of all my bread tasting the same. I just buy a loaf for the 2-3 times a year that I am craving a Reuben sandwich.