to inform (somebody) positively that something is the case
to give confidence to (somebody); to reassure
to guarantee the happening or attainment of (something); to ensure
A word in the right place would assure her promotion
(usu in passive) to make (something) safe; to insure (life, safety, etc)
assurer noun
[Middle English assuren via early French assurer from medieval Latin assecurare, from Latin as- + securus: see secure1]