I'll try to explain it more precisely than hazmat42:
16:9 aspect ratio says only that the picture frame is formatted to be displayed properly on the 16:9 tv screen. However, it is the special case of anamorphic format too.
Anamorphic format in general is independ from aspect ratio of the output TV screen and says what is the aspect ratio of the source film movie (it could be 2.35:1, 2.21:1, 1.85:1, 1.78:1, 1:33 or whatever else). The picture is encoded to the full resolution of the DVD format (720x756 pixels PAL, 720x480 NTSC) and the proper format of the picture is defined in the mpeg extension header as the "pixel aspect ratio" parameter. It means, how must be the square pixel of the encoded picture frame displayed as non-square pixel to obtain the desired aspect ratio of the movie.
For example (taking encoded is frame is 720x756 pixels PAL):
for anamorphic format 1:33 (4:3) the pixel aspect ratio is 1.067
for anamorphic format 1:78 (16:9) the pixel aspect ratio is 1.422
for anamorphic format 2:35 (most cinemas) the pixel aspect ratio is 1.881
etc...
If you play the anamorphic encoded movie on the TV, than according tho TV screen aspect ratio adjusted in DVD player menu, the player will at first fit the width of the picture on the screen, than will calculate the height according pixel aspect ratio and finally the rest lines will be filled black to get the letterboxed picture.
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