To the point:-
There are two electrons in a covalent bond.
Deeper meaning:-
A covalent bond can be meant of as a 'shared pair' of electrons, so there are 2 electrons in each bond. This means that a double bond will have 4 electrons in the space between the bonded nuclei, and a triple bond will have 6.
Hope it helps you...
(Answered by Benjemin)