Character, apparently means a whole list of things. Here are a few of them:

1.	the aggregate of features and traits that form the individual nature of some person or thing.

2.	one such feature or trait; characteristic.

3.	moral or ethical quality: a man of fine, honorable character.

4.	qualities of honesty, courage, or the like; integrity: It takes character to face up to a bully.

5.	reputation: a stain on one's character.

6.	good repute.

7.	an account of the qualities or peculiarities of a person or thing.

8.	a person, esp. with reference to behavior or personality: a suspicious character.

9.	Informal. an odd, eccentric, or unusual person.

10.	a person represented in a drama, story, etc.

11.	a part or role, as in a play or film.

12.	a symbol as used in a writing system, as a letter of the alphabet.

13.	the symbols of a writing system collectively.

14.	a significant visual mark or symbol.

Some others that I like:

Roman Catholic Theology. the ineffaceable imprint received on the soul through the sacraments of baptism, confirmation, and ordination.

in harmony with one's personal character or disposition: Such behavior is not in character for him.

And its origin:

1275–1325; < class="ital-inline">charaktr graving tool, its mark, equiv. to charak- (base of charáttein to engrave) + -tēr agent suffix; r. ME caractere < class="luna-Img" src="http://cache.lexico.com/dictionary/graphics/luna/thinsp.png" alt="" border="0">

I like the idea that a character can be represented (or created) by a mark that was left by an engraving tool... like a soul tattoo. So what is the character of a dream? What is the un-erasable engraving that marks a dream, and how could one represent it in music?

In my lesson we talked about the UNreality of it... that you're never quite sure whether it's real or not, but I'm not sure that's it for me. I think you can recognize a dream's UNreality by small but distinct markers that aren't separate from reality, but are weird in a normal, realistic context. Like Dali's dripping clock, it's not that it couldn't happen, it's just that it probably wouldn't. Those are physical things, though... what about the mental things that probably wouldn't happen? Like the running and getting nowhere, like the flying, like the knowing who somebody is even though you also know they look nothing like that person? So, if a dream does have a singular character made up of a series of characteristics, how do you musically represent it?