When you sit or stand astraddle something, you have one leg on each side of it. Kids on a seesaw sit astraddle as they bounce up and down.
The typical way to ride a horse is astraddle, with one leg on each side of the horse's back, and people also ride bikes and motorcycles while sitting astraddle. You might even have had a teacher or two who preferred to address the class while sitting astraddle the chair. Astraddle comes from the verb straddle, which comes from the same Old English root as the word stride — stridan, "to straddle."