Coif: A hood made from metal rings (i.e., mail), worn beneath a knight’s helmet
Ventail: A piece of mail that protected a knight’s throat and chin
Here's an example of a mail coif
(from CAS Hanwei)
Here's one example of a ventail in the form of a diagonal flap that tied onto the coif to protect the lower part of the knight's face. This flap could be square as well as diagonal.
(from Swords of Might)
That looks pretty uncomfortable, especially if all this hardware is worn underneath a metal helmet! Some drawings of ventails show them only covering the throat and chin, like this:
My hero, Etienne, preferred this style of ventail.
(Image from The Montague Millennium)
View some other parts of a medieval knight's armor from this September 16, 2009 Medieval Word of the Day entry.