Playing staccato or short means exactly that. Instead of letting the chords or notes ring out we cut them short using a combination of left and right hand muting.
To perform strumming hand staccato you strum the string as normal then place your hand on the strings to stop them from ringing. See Pattern 1 in the video.
To play left hand (fretting hand) staccato you play the note or chord as normal then quickly lift up your fingers so your not pressing into the fretboard anymore, but (and this is the important bit) you can still feel the string on your fingers.
Staccato is one of those techniques (like accents) that is used a lot, but the most important thing when you're learning is to be aware of when it's happening in the music.
Staccato is written in TAB with a dot under the note. (not beside the note, that's a dotted beat) See the sheet below for examples.