When beside the note, the "X" stands for a "double sharp". I recalled that from looooooooong ago, and had to make sure. Instead of going up a 1/2 tone it is a whole tone. The double flat was 2 flat symbols side-by-side. I always wondered why not just write the note in the proper location instead using double-sharps or double-flats... lol
To chase this digression a bit past what's reasonable, in order to answer a commonly-asked question: one typical reason why a double-sharp or double-flat might be used, instead of "writing the note in the proper location", is that it makes better sense from a "music theory" sense (the "math-y" side of music), in the context of the given key. Maybe for a brief moment a piece flirts with the key of, say, G♯ major, which has more sharps than notes in the key ("8" sharps, with the "8th" going to F♯, which... was already sharped). So you get an F𝄪 - an "F double-sharp". Now you could use a G natural instead, and you might imagine that leads to easier readability... but that's debatable given that we're momentarily in G♯, and are very likely to be playing that note too. So if both are occurring multiple times in a single bar, you end up naturalizing and re-sharping that poor G several times, versus double-sharping an F once (most likely the G will already be sharped in the key signature, in this scenario). Then you can write the F and the G as many more times as you want in that bar, without having to add accidentals every time.
But even when it only occurs once, the double-sharp may be selected simply because it's more "correct" from a music theory POV.
An astute reader might wonder what the hell we're doing in "G♯ major" in the first place, or anywhere near it, when there's a perfectly good A♭ to be had. But suffice to say there are "journeys" you can take from one key to another, where picking a crap key like G♯ momentarily is pretty much the best of an array of less-than-fantastic choices.
Alternatively, sometimes the double-sharp is just convenient, simply for an "avoiding constant accidentals" scenario like the one above, even when it's theoretically "
wrong" for the given key.