Does mopping floors actually clean them?

After a recent swap we came home and cleaned our floors with a wet and dry vacuum cleaner which involves scrubbing them with a bristle sweeping brush and sucking UP the dirty water and detergent. The water was a filthy as ever.

Do you mop floors? And how does a mop lift the dirt as opposed to merely diluting it and spreading it around the floor more evenly?

Why you should never clean the floor with a mop and bucket, according to the Hygiene Doctor | Ideal Home