This abbreviation means, literally, “and other things.” Many professors urge against using etc. in formal writing because it is, by definition, nonspecific, but it can be used effectively when you have responsibly chosen representative constituents in order to avoid a cumbersome list:
All prime numbers between 1 and 101 (2, 3, 5, 7, 11, etc.) were transmitted by the pulsing signal in the movie Contact.
Tacking on “etc.” at the end of a list introduced by “for example” or “such as” is sloppy, because “for example” suggests that you have already carefully selected and presented the key constituents, which the “etc.” then undermines. Good alternatives to “etc.” are “for example,” or “such as” followed by just a few concrete representative examples that best demonstrate your point.