Definition: The transition interval is the concentration range of a chemical species that can be detected using an indicator. Usually this refers to an acid-base (pH) indicator color change, but the same principle applies to fluorescence or any other visual indicator.
Examples: In a titration, the transition interval represents the concentration of a chemical required in order to see the indicator. Below this point, the intensity of the indicator may be too pale or dilute to detect. Similarly, if an upper limit is given in the transition interval, you won't be able to see a color change or other evidence of the indicator, either.