Learn Finnish: Sukkahousut ovat märkiä.

Because the subject sukkahousut is plural. When a plural subject is described by an adjective using the verb olla (to be), that adjective usually goes into the partitive plural. This shows you are describing a state or quality of the subject.

Could I use the nominative plural märät instead?

Not for this meaning. If you said Sukkahousut ovat märät, it would sound like an absolute identification, meaning something like "The tights are the wet ones" (out of a specific group). To simply describe the condition the tights are in, you need the partitive plural märkiä.

Is sukkahousut a plural-only word like "tights" in English?

Exactly. Just like the base word housut (pants/trousers), sukkahousut is almost always used in the plural. That is why it has the nominative plural -t ending, triggers the plural verb ovat, and requires the plural partitive complement märkiä.

How is the partitive plural märkiä formed from the basic word märkä?

The dictionary form is märkä (wet). To make it partitive plural, you drop the final -ä from the stem, add the plural marker -i-, and then attach the partitive ending -ä. This gives us märkiä.