Glissando, a musical slide.
Jo Ann is definitely glissing, but there's also
melisma, but that's more for stretching a syllable over a series of pitches. Billy Joel singing
Allentown springs to mind for some bizarre reason.
In current music, melismas definitely rule. Glissandos, like Jo Ann's, hark back to grand opera traditions (even grander than the "Grand Ole Opry"
).
Although, now that I type it, I'm realizing that
auto-tune is bringing glissandos BACK. All these pop tune choruses suddenly scooping up 8va (or 15va, yikes). Hah, what goes around comes around.