Diatonic intervals for ocarina
Diatonic intervals are the intervals that can be formed within a single scale, without the use of chromatic notes. It's easy to see how you can form them if you take the notes of a scale, and write them in a line:

We can form intervals from these notes by starting at any note, and counting forwards or backwards by some number of steps. The interval between C and E is called a 'diatonic third', as we are counting the notes, not the steps between them.
Practising diatonic intervals is valuable because it trains you how to move around the notes on your instrument in larger steps, both with regards to the changes in fingering and the breath changes needed to maintain good intonation.
Diatonic thirds

Diatonic fourths

Diatonic fifths

Diatonic sixths

Diatonic sevenths

Diatonic octaves

Other scales
Practising intervals is universally helpful to learn how to move around a scale in leaps, and the same idea can be applied the various minor scales, a blues scale, or pentatonic scale. Just write out the notes in a line, and form intervals between them.
When playing intervals from a scale that starts in the middle of the ocarina's range, perform them going up, then down, then up again:

We also have an interval generator tool to help you practice them with audio reference, supporting many different scales.