Does Mars have water?
Yes, although almost of of it is frozen as ice, buried below the surface.
Mars has a north and south pole; both have frozen water ice. During its winter the north pole gets covered in a layer of carbon dioxide ice about 1 metre thick, which then sublimes1 and exposes the water ice in summer. The south pole is permanently covered in a CO2 ice layer about 8 km thick, so its water ice is never seen on the surface.
Around the more temperate areas of Mars there are also large deposits of underground ice.
Mars may have some small pockets of underground liquid water in the form of very salty brine. It's possible that small amounts of this brine may occasionally exist for a short time on the surface.
Mars has a very thin atmosphere which does have small amounts of water vapour and occasional water ice clouds. It is the thinness of the atmosphere that makes it impossible for liquid water to exist on the surface—if the water doesn't freeze it evaporates.
There is very strong evidence that Mars had a lot of liquid surface water in the distant past, including rivers and oceans. In those days Mars had a thicker atmosphere so water could remain liquid. These days, however, most of Mars is very dry and people would have to drill into the ground to find any usable water.
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Footnotes
[1] Sublime means turn directly from solid to gas without going through the liquid stage (melting) first.