Play D13 one string at a time and you hear D, F#, A, C, E and B. D is the root, F# the major third, A the fifth, C the minor seventh, E the ninth and B the thirteenth. Said aloud, its notes are D, F sharp, A, C, E and B.
String by string, low to high, it plays D, C, F# and B. This shape drops two chord tones, A and E. They are the fifth and ninth. It runs from D on string 6 up to B on string 2.
D13 uses no barre and no open strings, so you can slide the shape up the neck without changing fingers. Strings 5 and 1 stay silent. Your hand covers three frets, from 10 to 12. There is one more position, starting at fret 5.
Inside D13 sits a complete Bm chord, made of D, F# and B.
D13 belongs to only one key, G major, where it is the V13.