Binding is when you bind your breasts so they're tight against your chest and it appears you have a male chest. (Someone might be able to give a better definition, but I think that gets the idea across.)
^^ This is pretty much what binding means, provided that the conversation is about transmen (FtM) or butch women, or any female-bodied person who might want to appear more masculine. In other contexts, the term has other meanings. I have no idea what you watched on youtube, so I can't tell you for sure.
Then, yes, "binding" refers to binding one's breasts so that they appear as flat as possible, usually in order to achieve a more masculine appearance. ***Please be careful about binding your breasts, as some methods of doing so can cause serious health problems, as can binding too tightly.*** Breast binding safety
