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I quote wiki :

Soon after Newton had obtained his B.A. degree in August 1665, the university temporarily closed as a precaution against the Great Plague. Although he had been undistinguished as a Cambridge student,[15] Newton's private studies at his home in Woolsthorpe over the subsequent two years saw the development of his theories on calculus,[16] optics, and the law of gravitation.

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    He was only 23 - perhaps he simply camped-in at his mother's.
    – Pieter Geerkens
    Commented Mar 26, 2014 at 22:16
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    Newton returned home to Lincolnshire during this period and was supported by his mother, Hannah Ayscough. When her second husband (the wealthy clergyman Reverend Barnabus Smith) died in 1653, she was was left with a good bit of wealth and property.
    – David H
    Commented Mar 30, 2014 at 0:02

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These years are typically referred to Newton's "Golden years" due to the quantity and quality of his works during those years. Newton's Mother and Uncle managed the farm through out Newton's life. During the plague his family would have taken care of him, like provide him food clothing and shelter. His family knew that he was an "absent minded farmer" which is why his uncle initially sent him to Cambridge to study.

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    "Isaac Newton: Man Myth and Mathematics" by V. Frederick Rickey
    – Samantha Hutto
    Commented Apr 21, 2016 at 0:39

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