It could mean palm muting, if you have a video it is easy to verify, but most of the time it means quieter (piano). Double "pp" means even quieter (pianissimo). Mind you, that is kind of what a palm muting does so you won't be far off except it will sound very compressed as well.
Regarding ghost notes (crosses on the TABs) you just play them by lifting your finger so that it does not touch the fret board, just resting lightly on the string.
If you know how to do harmonics, this is basically doing the same except your finger is not somewhere on the string where you can hear harmonics. If you rest your finger right in the middle of the string (fret 12) then you will hear harmonics instead of a ghost note.
It generally happens incidentally in 2 cases. One is when you strum a chord but you want to ignore a string in between 2 strings. You have no choice but to rest your finger on this string so that we don't hear the open string.
The other case is when sometimes when changing chords people play the open strings while moving to the next chords to avoid a blank. But when the open string notes are not in the key they are playing in, it can sound disgraceful. Then in this case they might rest their fingers so that we hear ghost notes instead.
And then obviously ghost notes can also be stylistic like the ones in "Smells like teen spirit" main riff.