This is an abbreviation of the Latin et cetera, meaning 'and other things'. Some people say that it should not be used with lists of people, or to mean 'and so forth' when referring to events or actions: The children laughed, shouted, ran about, etc.
However, its use in these contexts is well established, although et al is more polite when referring to people (this is an abbreviation of the Latin et alii, meaning 'and others').
The more important question is whether you should use these abbreviations at all. They are useful for notes and on forms, but look out of place in ordinary writing; better to begin a list of examples with such as or for example, or to follow it with and so on, and so forth, or (with people) and others.
Whatever form you use, make sure that you give some idea of what the other items might be.
In a sentence such as there are worms etc in the garden, etc could refer to almost anything: worms, beetles, woodlice, and so on suggests other creepy-crawlies, while: creatures such as worms, spiders, and frogs suggests a much wider range of wildlife.
This means that you have to know what you mean: etc and its equivalents are often used when people are not sure, or cannot be bothered to think about, what they wish to include. Remember the c in et cetera is pronounced s. The et is sometimes incorrectly pronounced ek. Note also that etc and et al can be written with or without a full stop.