etc. is short for "et cetera" (pronounced ett setera). It is a Latin expression that is used at the end of a list to indicate that further, similar items are included. For example, you could say "I am going to the shop to buy milk, eggs, ham, bread, etc." or "I like sports, such as swimming, football, hockey, etc.". It is mostly used in writing, but people do often say it when speaking too.

Ellipses (...) can refer to additional items in a list mentioned. In verbal speech, it is closest to saying "and so on".