Since hay is the resultant of mown grass dried for fodder, and the sun is the cheapest and most available drying agency, the literal sense of the aphorism “to make hay while the sun shines” is most obvious.
Its figurative intent is equivalent to “Strike while the iron is hot,” and in fact such are both the German and French phrases: Das Eisen schmieden solange es noch heiss ist, and Battre le fer pendant qu’il est chaud.
That is, the English phrase means, if an explanation is needed, to seize opportunity by the forelock; to take advantage of a good thing before it slips past.
John Heywood in his All the Prouerbes in the Englishe Tongue (1546) gave it: “Whan the sunne shinth make hay.”
