A "sextet" atom has a lack of electrons and is eager to get 2 additional valence electrons to fill its octet. By a Lewis acid-base reaction (between ether and BF3) or lone-pair donation from a neighbouring atom (the mesomeric structures of the two carbocations), another bond with 2 electrons to the sextet atom is made and its octet is completed.
In an element of a compound, when the number of electrons in the valence shell is equal to 6, it is called sextet of electrons.