An offshore company is simply a company registered in a jurisdiction other than the one where you live. It does not have to be a tax haven.  For example, if I lived in Canada, I could incorporate an offshore company in Mexico.  I may not actually want to do that but it would fit the definition of an "offshore company".

There are a great many benefits to be found when considering the incorporation of a company  offshore.

An offshore company or non-resident company, is a company that does not conduct a large portion of its business in the the country it is incorporated in.