Learn Polish: Być może będzie padać.

Both mean "maybe" or "perhaps." Być może (literally "to be it can") is just a slightly more formal or emphatic fixed phrase, often used at the beginning of a sentence. You could easily say Może będzie padać and the meaning would remain exactly the same.

Where is the word for "it" in będzie padać?

Polish doesn't use a dummy pronoun like "it" for weather expressions. While English requires you to say "it will rain," Polish simply pairs the third-person singular future verb będzie (will be) with the action. Adding a word like to or ono here would sound unnatural.

Why is padać in its dictionary (infinitive) form here?

This is how you build the future tense for imperfective verbs (verbs describing ongoing or repeated actions). You combine the future form of "to be" (będzie) with the infinitive of the main verb (padać). So, będzie padać expresses that the raining will be an ongoing action in the future.

I thought padać meant "to fall". How do we know it means "rain" in this sentence?

You are right that padać literally means "to fall." However, when used all by itself in the context of weather, it is universally understood to mean "to rain." If a Polish speaker wants to say it will snow, they usually add the word for snow: będzie padać śnieg (snow will fall).