Paperwork for Work Visa (Bogotá)

I'm a little confused on the process for teaching English. I read another post but I'm still confused. I know I need my bachelor's degree and TEFL/TESOL certificate notarized. But what is this apostilled process thingy? I've never heard of it before. Can someone tell me what it is and where I can go to get it done in the US.

Also, do you have to do the same thing for your vaccination records? Thanks.