Why "a work out" needs a workout in grammar

What kind of error is it?

It's a lexical and grammatical error involving word separation.

Why do people make this mistake?

People often confuse the noun "workout" with the verb or verb phrase "to work out" leading them to incorrectly separate "workout" into two words.

What is correct?

"Workout" is the correct noun form when referring to a session of physical exercise. The phrase "work out" refers to the verb form meaning to exercise.