"Why invert? I thought you'd never ask! There are many reasons. In common practice, chord progressions are not generally successions of root position chords moving one to another (except in heavy metal music, in which whole songs of only root position chords, are commonly the case). In most other types of music, progressions are made up of individual chord-tones moving independently from notes in one chord to notes in the next chord, creating melody lines, which are often called voices, because the resulting melodies could be sung or played by individual instruments. So, chord progressions (any series of chords) sound better with root position chords mixed with inverted chords, so various notes of one chord lead smoothly to notes in the next chord, with others perhaps not moving at all. This is called voice leading.
Another reason for inversion, especially important for string instruments, is to make the chord easier (or in many cases possible) to reach. Many chords- especially ones with four or more notes- are virtually unplayable in root position on instruments such as guitar and mandolin." -- Edly