In Walter's Guide to the Magus,
https://docs.google.com/document/edit?id=1DB6sOfbAzFmKVPgcyLWipTVqvWFjfDSv6 v_YiGQb5Yw&pli=1
the following is claimed:
"Note though, that Arcane Mark enables you to Spell Combat / Spell Strike each round with your weapon and essentially gain a free attack. Think of it like Flurry of Blows with a scimitar."
Spell combat allows you to make a melee attack and cast a spell as if you are two weapon fighting, and spell strie lets you channel a spell cast (so long as it has the range of touch) through a weapon.
How does this give you a free attack? It seems like you get to make your normal full round action attack routine, but with arcane mark cast through one of the attacks.