The notion is that in the Garden of Eden, the original pre-Lapsarian world, there were no seasons but an eternal springtime. Then at a later date, God introduced the seasons as part of a general decline, which in the Bible is attributed to God's punishment of man for the sins of Adam and Eve in the Garden.
This is an old idea that goes back to Classical Rome. It's in Ovid's account of the four ages of man, in Metamorphoses book One (see Wikipedia). Ovid writes of the Golden Age
Western winds immortal spring maintain'd.
Then comes the Silver Age:
Then summer, autumn, winter did appear:
And spring was but a season of the year.
The idea of the different ages of man was a commonplace of classical Roman thought, but Ovid seems to have given it a particularly clear expression in a work that was widely read in the early modern west.
Renaissance thinkers linked this with the Biblical narrative of the fall of man, although Roman Christians may have made a similar connection long before (see Milton and the "Seasons' Difference", S. Viswanathan, Studies in English Literature, 1500-1900, Vol. 13, No. 1, The English Renaissance (Winter, 1973), pp. 127-133 on JSTOR).
Knowledge of the tilt of the earth's axis was known even before Classical Rome, to the ancient Egyptians and Chinese around 1100 BCE. Pytheas measured it in 350 BCE to a greater accuracy than what Milton cites.
It was known that the tilt of the axis was connected with the seasons (together with the different length of days and the height of the sun at noon). No tilt means no seasons. So Milton put all this together to link the tilting of the earth's axis with the Fall of Man.