Word for one character explaining to another character some important points for benefit of the audience

Solution 1:

What you're describing is expository dialogue.

More colloquially, it's also called an info dump or "as you know, Bob" dialogue.

The last term is generally used in a critical sense, referring to dialogue in a movie or tv show that is obviously unnatural and presented only for the audience's benefit. For example:

Dr. Smartly: As you know, Bob, giant robots have a universal weakness for high-fructose corn syrup, and I've been researching this in my lab. If a giant robot ever attacks Pleasantville, it's a good thing the soda pop factory is nearby...

[90 minutes later]

Bob Dogood (our hero): Eat sweet justic, infernal menace!