... was, according to a traditional anecdote, "an ill–favoured stallion, kept in the Mews, but remarkable for getting fine colts." The king himself had many mistresses and sired many illegitimate children ... and this is how the name came to be applied to him.
The anecdote (of which Wikipedia gives three versions, dating from 1769 to 1933) continues: "Mrs. Holford, a young lady of considerable attractions, much admired by Charles, was sitting in her apartment, and singing a ballad upon Old Rowley, the king, when he knocked at the door. Upon her asking who was there? he, with his usual good humour, replied, 'Old Rowley himself, madam.'"
Wikipedia gives the first verse of the ballad in question. If you read it, you may think that's more than enough to get the picture!
© Haydn Thompson 2020