Aldersgate Day is celebrated on May 24 (or the Sunday closest) to commemorate the day in 1738 when John Wesley experienced assurance of his salvation. Wesley reluctantly attended a group meeting that evening on Aldersgate Street in London. As he heard a reading from Luther's Preface to the Epistle to the Romans, he felt his "heart strangely warmed." Wesley wrote in his journal that at about 8:45 p.m. "while he was describing the change which God works in the heart through faith in Christ, I felt my heart strangely warmed. I felt I did trust in Christ, Christ alone for salvation; and an assurance was given me that He had taken away my sins, even mine, and saved me from the law of sin and death."
Charles Wesley only a few days before had also had a conversion experience in a building that still stands on an adjacent block (John Bray's house on Little Britain). We do not know whether the building where John Wesley's experience took place still exists, nor exactly in which building on Aldersgate Street it may have been if it still stands. A monument at the London Museum on Aldersgate Street marks where some believe the building may have been.
Over time, Aldersgate Street has been shortened by common Methodist usage to simply Aldersgate. The word has come to represent both the place and John Wesley's experience.
From https://www.umc.org/en/content/ask-the-umc-what-is-aldersgate-day?