When Mars is at its hottest - still cold enough to freeze water - the atmospheric dust can absorb the energy of the sunhght, which causes warm pockets of air to rapidly move towards colder, low-pressure regions, generating winds up to 45 metres per second (162 kilometres per hour or 100 miles per hour) that begin to pick up dust particles from the ground, adding to the atmospheric dust content and increasing heating, pushing the winds harder and faster until the atmosphere is filled by dust.
And then, just as quickly, the storm can die down. Perhaps by blocking the sunhght, the surface of Mars grows cooler, allowing some of the dust to begin sinking out of the atmosphere. Not all dust storms swallow the entire planet - some are more localised events. However, were you to be on the surface during a dust storm, other than the sky darkening and a fine coating of dust settling over you the atmosphere is so thin that you'd barely notice the wind or the scouring dust.