A dirt road is made up of dirt. Similarly, a concrete road is made up of concrete.

In English it is very common for nouns to be used as adjectives. There are no reliable rules. Dictionaries will call out the most frequent examples, but it is possible to use them that way even if they are not in a dictionary. The meaning has to be understood from knowledge of the world, not from grammar. As Alex points out, names of materials can be used as adjectives. There's no change in the form of the word. A dirt road, a gravel road, a copper kettle, apple pie (a dessert made from apples), a brick wall, a fur coat, leather shoes, steel rails. Unfortunately it's old technology, but "a cathode ray tube oscilloscope" contains four nouns in a row! The first three all are being used as adjectives. Cathode rays are rays that come from a cathode. Cathode ray tubes are tubes that are designed to produce cathode rays. A cathode ray tube oscilloscope is an oscilloscope that uses a cathode ray tube.

"Dirt" here refers to the substance of the road - mud and other natural substances. There is no surface, like asphalt. You also see "dirt track".

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