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Explain comes from Middle English explanen, from Old French explaner, from Latin explānō ‘to flatten, make plain’, from ex- + plānō.

1. Latinc. 75 BCE–200 CEplānus¹‘level, plain’
2. Latinc. 75 BCE–200 CEplānō¹‘to flatten’
3. Latinc. 75 BCE–200 CEexplānō¹‘to make plain, explain’
4. Old Frenchc. 842–1400explaner¹
5. Middle Englishc. 1150–1500explanen¹
6. Englishearliest quotation 1909explain¹

1. ¹ Wiktionary, English explain
2. Earliest quotation in Wiktionary’s entry: 1909, Archibald Marshall pseudonym; Arthur Ham, A Court Ball: “The boy became volubly friendly and bubbling over with…”.