Here's how it works:
As a noun:
* It refers to the Mediterranean Sea: "We sailed across the Mediterranean."
* It can refer to the Mediterranean region: "The Mediterranean climate is known for its hot, dry summers."
As an adjective:
* It describes something relating to the Mediterranean Sea or region: "Mediterranean cuisine is famous for its use of olive oil and fresh herbs."
So, the word "Mediterranean" is both a noun and an adjective depending on how it's used in a sentence.