Above is a staff. After the third bar, why isn't the second C either sharp or natural?
Accidentals (sharps, flats or naturals) only change notes until the end of the bar they are in. So, the C# above doesn't affect the C in the next bar. However, flats or sharps in key-signatures affect all notes in the music, for instance the Bb and Eb above, unless "overruled" by another accidental, for example the B natural above.