Yes, there is friction on Mars, and it functions the same way that it does on Earth, but the values are likely to be different on a case-by-case basis.
Friction is basically the result of matter interacting with other matter and causing both bodies to alter their momentum. Fundamentally, this is due to the electrons on the outside of atoms coming into close proximity to each other, and repelling each other proportionally to that proximity. At a slightly larger scale, it can also be due to imperfections in a surface that provide relatively jagged edges that another surface would catch on, deflecting its motion. In simple terms, as long as there's something for an object to bump into, there will be friction.
Mars definitely has a surface, and it also has an atmosphere, albeit a thin one, so there's definitely friction from both the surface and the air. However, the density of the air is much lower than the Earth's, so the air friction is lower. Likewise, Mars' gravity is about a third of Earth's, so the force with which any objects on the surface would be "squeezed" against each other is much lower, meaning that there would be less friction there too.
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