На улице было влажно, и пододеяльник сох дольше, чем наволочка.

to be

Breakdown of На улице было влажно, и пододеяльник сох дольше, чем наволочка.

• и: and
• на: on
• улица: the street

Questions & Answers about На улице было влажно, и пододеяльник сох дольше, чем наволочка.

Why does the sentence start with На улице, and what case is улице in?

На улице means outside / in the street / outdoors (depending on context).
улице is in the prepositional case (locative meaning), used after на when it means “(located) on/in a place”:

• на улице = outside / on the street
  Compare:
• в комнате = in the room
• на улице = outside (literally “on the street”)

Why is it было влажно and not something like была влажная?

было влажно is an impersonal predicative construction: “it was damp.”

• было is past tense neuter singular because there is no grammatical subject like “it” in Russian here.
• влажно is a predicative adverb/state word (category of state), describing the general conditions.

If you wanted an adjective, you’d need a noun:

• На улице была влажная погода. = “Outside the weather was damp.”

Is влажно an adjective or an adverb here?

In this sentence, влажно functions as a predicative word (state), not a normal adverb modifying a verb and not an adjective modifying a noun. It answers “what was it like (in general)?” → “damp.”