A chord doesn't have to be played with its root at the bottom. As long as the same notes sound, it's the same chord; only the order changes. That changes how it sounds, and how smoothly it connects to the next chord.
How you arrange a chord's notes (which is lowest, which is on top, how close together) is called its voicing. Inversions are the first step.
Move the lowest note of a up an octave and you get an inversion. So a triad can be played three ways: root position (root at the bottom), 1st inversion (3rd at the bottom) and 2nd inversion (5th at the bottom).
The lowest note of a chord is called the bass.
The inversions are written as slash chords: C/E means "C major with E in the bass".
Inversions let the bass move in small steps instead of jumping. Play C, then G with B in the bass (G/B), then Am: the bass walks down C, B, A, and the chords flow into each other.
Guitarists often play triads on just three neighbouring strings, called a string set. Each inversion gives its own little . Here is C major on the D G B strings (filled notes are the root C), sorted by fret. The shapes chain up the neck: 2nd inversion at fret 5, root position at fret 8, 1st inversion at fret 12, then the same order starts again 12 frets higher.
Learn the three shapes on one set of strings, and you can play any major chord anywhere on the neck, just by sliding them.
Next: Power Chords