What is the meaning of that wavy vertical line in the guitar tablature shown in the image?
It's an arpeggio, or perhaps more precisely, an arpeggiated chord. You play the notes in rapid succession, from the lowest to the highest. The symbol is the same in traditional sheet music.
Note that it is not a "broken chord" arpeggio: it should be thought of as a single chord, each individual note struck rapidly after each other (you could, possibly, just use one finger to strike across the note, though I think the more classical technique just uses all fingers one after the other).
Traditionally, the direction is lowest to highest note. If it's the other way around, a down arrow will be drawn just before the arpeggio symbol. And in some music, both explicit up and down arrows may be drawn (if the direction changes a lot from arpeggio to arpeggio).
Simply: Strum but not quite as fast as normal.
This is also used in piano music where the musician is instructed to play the chord "strummed" in that the notes are played in rapid ascending order but still held as one chord. In this case, move up the strings over the course of about half a second to a second. It needs to be fast enough to still be a strummed chord but not so fast as to just be a normal strum.