This two-part video tutorial series presents a breakdown of applied music theory on the ukulele.
In the key of C major you have the notes CDEFGABC. The notes C to C give you C major(or Ionian). The notes A to A give you A minor (or Locrian). The notes G to G give you Mixolydian and the notes E to E give you E Phrygian.
Playing the C major scale from D to D gives you D Dorian, F to F gives you F Lydian and B to B gives you Locrian. These are just names for organizing the Major scale. The tonality of the notes played are relative to the chord being played and the scale notes that are emphasized.
For more information on applying music theory to your uke playing, watch this free video lesson.