Explanations varied. Scientific explanations were typically based on the reflection of light, from either raindrops, or clouds, or mist in the air (raindrops being correct). Exactly how reflection gives rise to a bow was explained by Theodoric of Freiberg and Kamal al-Farisi c. 1300. Explaining how the colours arise is post-Medieval, courtesy of Isaac Newton.

There were also various magical/mythological explanations.

For more, see my past answer in https://www.reddit.com/r/AskHistorians/comments/c0wone/what_did_ancient_people_think_about_rainbows_and/