A tritone is an augmented fourth or diminished fifth interval found between the subdominant and the leading tone of a scale. It is considered to be the most dissonant of all intervals and has thus very specific treatment.
When heard melodically, a tritone is resolved by melodic step inwards. That is to say if a melodic line leaps to an interval of a tritone it should resolve by moving stepwise in the opposite direction of the leap.
When heard harmonically, the tritone typically resolves to a third or a sixth. The character of this interval (i.e. major or minor) would be determined by the key of the piece. The subdominant scale degree descends to the mediant and the leading tone rises to the tonic.
The tritone is an especially important interval as it appears naturally in a dominant seventh chord. It is the combination of the fifth relationship between the dominant and the tonic and the juxtaposition of the dissonant, unstable tritone with the consonant, stable third or sixth that makes the dominant seventh chord so effective.