I think Tu means your, and Tú means you. Compare Él (he) and El (the)...

What Vidde said. Accents in Spanish have two main functions: 1. To mark stressed syllables if they deviate from the standard stressing rules and 2. to disambiguate between homophones (words that sound alike but have different meanings). At least in case 2 it may help to consider 'ú' as a completely different letter from 'u', not just a 'decorated' version of it.