Dreams are the touchstone of our character.

Literal

Dream [topic-は] our [possessive-の] character [possessive-の] touchstone [copula-である].

試金石 ('touchstone') is a metaphor for a test that reveals true quality — originally a stone used to test gold purity, now the standard Japanese metaphor for a character-testing situation. である is the formal copula. An aphoristic/philosophical statement.