Et cetera is the full form of ETC. Et cetera is a Latin word which 'means and so on' and 'and other things'. We generally use Etc at the end of a sentence especially when we are making example of some things, the moment we include etc, it means you are referring to other examples that are related to what you are discussing.
For example, the following are the examples of stationery; book, pen, pencil, eraser etc, the etc you included means other examples of stationery materials you can think of. It is being used most times to shorten the continuity of a sentence especially when you are listing items.
The word 'Et cetera' has been adopted from Latin to English and it's short form is etc. Also, etc is used when you have more similar items in series or list and you don’t want to mention everything, then you can use the word ETC.