In a general sense, that pattern is simply referred to as "open fifths." (It has other names too, such as a {0,7} unordered pitch class set). Sticklers might argue that this is not a chord at all but an interval with one note doubled.
It's common because the notes are harmonious with each other even in lower ranges. A full chord in the bass sounds very muddy, but leaving it "open" allows the notes to ring a bit clearer. You will see open fifths in the left hand whenever a chord is in the "open position" meaning the notes of the chord are spaced out for a more open sound. Another common left-hand pattern is 0-5-10 (C1,G1,E2) which also has a pleasant open sound but is more difficult to play as it requires your left hand to stretch to a 10th.
So that explains left hand open fifths, but why does this pattern show up in the right hand as well? Well, an open fifth is a lot like a triad that is missing its third. Some chords, however, have their third in the bass (this is known as a 6-3 chord, named after the size of the intervals above the lowest note). When there is a third in the bass it is very difficult to double it without introducing parallel octaves, which is considered poor voice leading in much of western music. So if there is a third in the bass, the right hand is often playing open fifths. You'll find this pattern all over the place in the scores of Mozart and Haydn.