A macro is pretty much just a little script that can make you client to do a serious of tasks, from something as simple as saying something in chat to things like automatically farming or repairing your tools when they get low on durability.

 

Wiki link for macro.
When people are talking about macro on the forums they are generally referring to the macro mod for minecraft. Macro programs and scripts can be used in many, many other programs such as internet browsers, word, notepad++, other video games, etc.