Definition - The clause in a conditional sentence that expresses the consequence.
Note: The clause that expresses the condition is called the protasis.

Example -
In the sentence If you loved me back, I would love you forward:
(1) the protasis is If you loved me back and
(2) the apodosis is I would love you forward

Etymology -
The word derives from the Greek apodidomi, give back (from the Greek apo, from or away + didomi, give).

Oxford English Dictionary -
Its first citation is from 1638:
"Let us consider a little of the Protasis
[‘Even so hath the Lord ordained, that they which preach the Gospel’],
whereof the words I have now read [‘should live of the Gospel’] are the Apodosis. "
(Mede Wks. i. xxi. 77 )

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