Hi ! As a non native speaker, this is the way I understand this verb. Let's see if a native speaker confirms it or not and / or can give us some more detailed information. The meaning is that of "being able", sometimes even "to manage (to do something)". A certain effort or strength seems to be implied and / or underlined with this verb : - er vermag es nicht, mich zu überzeugen (he can't / doesn't manage to convince me) - nur wenige vermochten sich zu retten (only a few could / manage to escape) - wir werden alles tun, was wir vermögen (we'll do all that we can = that is in our power or abilities). The idea of "achieving smth" can be found in such sentences : - Geduld vermag viel bei ihm (Patience "can" a lot with him = plays an important role to get what you want / need from him) It is true that I've hardly ever met this verb in my experience. Only in older literary texts.

As Susanne said correctly above, this is an old fashioned word that is used in ancient literature but rarely in modern German. It is also used in the Bible in a literary form. Instead of using "vermögen," modern German uses "können" instead. Er vermochte es nicht mich davon zu überzeugen. This would be today: Er konnte mich nicht davon überzeugen.

This is such an old-fashioned verb that I'd strongly advise you not to use it at all! I don't think I've heard it in my life, I've only ever read it in old books, e.g. "Er vermochte die schwere Tür nicht zu öffnen" = "Er konnte die schwere Tür nicht öffnen"; "Ich vermag es nicht zu sagen" = "Ich kann es nicht sagen"