This TAB notation shows a typical way to play octaves on guitar. As it is not possible to play an octave on adjacent strings (because the stretch would be too big at 7 or 8 frets) an octave is typically played on a pair of strings which have an unplayed string between. This is easy to do fingerstyle, when playing classical guitar, for instance, but is more difficult with a pick, as you have to make sure the string between the notes you want doesn't sound.
So, you have to damp (or choke, or mute) this string. This is what the 'x' denotes. This is actually pretty easy to do; you use what I call "lazy technique" when describing it to my pupils! Usually, when playing chords on the guitar, you want to try not to touch adjacent strings with your left-hand fingers when fingering chords, in order not to stop any notes sounding (barre chords being an obvious exception). And so, you usually try to keep your left-hand fingers pointing straight towards the fretboard. In order to mute the string between the octave notes, though, you let your left-hand fingers flatten slightly (approaching the string at a 45 degree angle, or even flatter) so that they damp the muted string. Usually, this means that the index finger on the left-hand will damp the string between the octave notes (the string with the 'x' marks).
However, you can actually damp the string below the bottom note of the octave with the tip of your index finger; you can also damp any strings above the top note of your octave with either a combination of fingers, or just the finger playing the top note of the octave, so you can actually strum all the strings! This gives a great, percussive sound, and means you can really go for it with your strumming.
I'm a bit lazy, so I use fingers 1 and 4 for octaves most of the time, whether I'm stretching over 3 or 4 frets. In the picture below, I'm damping string 6 with the tip of my index finger, damping string 4 with my index finger, damping string 2 with my pinky and damping string 1 with the first joint from the hand of my index finger. And this is done while playing the octave notes on strings 5 and 3, with index and pinky fingers respectively.
Sorry it's a bit hard to see what I'm doing in the picture, I'm not very good at taking pictures of my hands while fretting! (At least you get to see my cat, though...)
So, the octave I'm fretting above can actually be written like this:
Just to be clear, you only actually need to damp the string between the octave notes, but this does mean you need to play reasonably carefully with the pick, so that you only strum three strings. If you damp more strings, you can go mad with your strumming, Pete Townshend style (windmill away...!)