Em/D gives the bass its own instruction: keep the upper chord, but make the lowest note. The slash separates those two jobs.
D is not in the upper triad; it completes a minor seventh chord with its flat seventh lowest. Hold the upper chord steady and move only the bass. That low line can connect nearby chords without jumping root to root.
Also written Em over D or Em with D in the bass.

In which keys. Every note of Em/D belongs to C major (the iii), D major (the ii), E minor (the i), G major (the vi), A minor (the v) and B minor (the iv).
Contains Em/D and adds eleventh.
Contains Em/D and adds eleventh and sharp eleventh.
Contains Em/D and adds ninth, eleventh and flat thirteenth.
Contains Em/D and adds ninth, eleventh and thirteenth.
Contains Em/D and adds flat ninth, eleventh and flat thirteenth.
The common shapes and the derived voicings come from different places, and both are explained in how this site is built.
Shows each chord the way this style would voice it, and marks which of its alternatives belong to the idiom.