In other words :
standard DVD resolution is 720x576(PAL) or 720x480(NTSC).
If you want to encode a widescreen picture to DVD, you can

pan and scan it and encode with “4:3” flag - thankfully not done anymore (I hope), basically cutting the left and right parts of the frame and moving the visible part so that you can see everything “important” in each scene
encode as a 4:3 image with black bars at the top and bottom, this is how the GOUT DVD is encoded. On a 4:3 TV it looks correctly, but who still uses a 4:3 TV in 2017 (except me in my bedroom)? On a 16:9 TV you get black bars on the left, the right (both generated by the player because you are projecting an “almost square” to a rectangle), and on the top and the bottom (actual part of the 4:3 image). So you have to find some other way how to crop the borders and stretch the visible middle part (usually TVs have a special mode for it), but it usually looks pretty bad
stretch the image and encode it with the 16:9 flag, this is what anamorphic DVDs do. The actual image is taller, but because the player knows it is supposed to be 16:9, it will stretch it automatically. Usually this leaves us with much better looking picture, because we had more “lines of information”