Railroad is a commonly used transportation system on Earth, and it can be used on Mars as well. Iron as the main construction material is abundant on the Martian surface. Compared with most other transportation systems, the railroad is basically lo-tech and can, therefore, be maintained with low effort.
Compared with rovers a railroad system is rather inflexible, but it can have an advantage for frequently used ways. On the long run it allows energy optimized transport. No batteries or fuels are necessary if electrical engines are used. Especially for driverless material transport it can be a central part of the settlement's infrastructure.
Elon Musk's initiative to develop the hyperloop technology allows the anticipation of a very similar transportation system on Mars. Compared to the terrestrial concept it would require only a thin-walled tube. The air pressure in the tube would be slightly higher than the surrounding Martian atmosphere, preventing the invasion of dust. Musk himself imagines a version without a tube on Mars.
The transport of a maintenance team
Peripheral parts of a Martian settlement might be several kilometers away from the living quarters. Energy generating stations (e.g. solar panels, wind turbines) are spread over a large area. A light weight railroad system reduces the maintenance costs on the long run.
Transportation in tunnels
Parts of the colony will be underground. During mining activities a railroad system provides a comfortable transportation of material and persons over long underground distances.
Connection between two settlements
Railroad covers both short and long distances. Even in the far future with more than one settlement on Mars, people will still be interested in efficient transportation systems. Only a magnetic levitation system might have a better energy balance.