I have been wondering whether there is a term for the technique singers use when they sing one syllable of text over a large number of different notes very quickly. There are examples of this in Händel's operas. Since this technique is used within a syllable and there are no consonants available to separate the notes from each other, it often sounds as though the singer is singing an 'h' to facilitate the separation of pitches.
This answer actually has two parts:
Melisma is when a vocalist sings multiple pitches on one syllable. When you hear music in this way, you would say that the music is melismatic.
Coloratura is a "coloring" of musical figuration meant to embellish the musical line. In Handel's time, much of the embellishing was improvised over the written line. It also concerns how the melisma is used in the music.
I would like to expand on @jjmusicnotes' answer.
When a number of notes for one syllable are written out in the sheet music by the composer, the term used to describe this is melisma.
When the performer chooses to add additional notes in an improvisational manner (notes which are not written out by the composer), the usual term for this is ornamentation. Ornamentation is a common element of music from the Baroque period, such as that by Handel and Bach, and certain kinds of ornamentation are used by singers and solo instrumentalists alike.
The term coloratura is not often used in this context; rather, the term "coloratura" is usually used to describe a soprano singer with an unusually high range of notes who is often found singing music with a lot of melisma or ornamentation in it.
The adjective form of melisma is melismatic. From the academic standpoint, you often hear the term "melismatic" also used to describe the florid style of singing found in American R&B music by female singers such as Whitney Houston or Mariah Carey, who are known to sing a lot of melodic notes on a syllable. So the melismatic style is found in other places besides Western classical music.
Those are called coloratura. There is even a voice category "coloratura soprano" named after them.