What is "For the better or worse"?

What is for the better or worse? I remember hearing this a few times before but am not really 100% sure on the exact meaning of it.

Usually this is said, "for better or (for) worse" (without the). This phrase is used to indicate that a fact you are mentioning is not necessarily a good thing or bad thing. Often it is used if you say something, and you do not want to imply that you think it is a good thing.

Nowadays, anybody can easily publish articles on the Internet, for better or worse.

The idiom is "for better or worse" - is it this you mean? If so, it just expresses this:

If a situation exists or happens for better or for worse, it exists or happens whether its results are good or bad.

See here.

This comes from an idiom "for the better/worse", which means "to produce improvement/decline".

If this is not what you are looking for, there is a phrase "for the better part", which means "for more than half but not all". This is used sometimes like: "for the better or worse part [of my life]", which would be "more than half my lifetime, but using better is somewhat misleading, as the time really was not good, but bad".