what is the advantage to having a DVD player that has an "HDMI" outlet on the back vs. the audio, video, etc plugs on the back?

For a DVD player, it's more convenience to suit the connections teh TV has, and may not make much difference as DVDs are not high definition to start with.

The DVD video format was created for "standard definition" 525 or 625 line analog TV systems, pre HD.

HDMI will theoretically still give fractionally better quality with DVDs, as the whole system is then digital all the way from the disc to the screen, rather than being converted to analog and back again.

HDMI is much better with material that starts out in high definition, such as BluRay; with good source material and a good HD TV, you would see a significant difference in image sharpness and detail with HDMI compared to analog AV.

For SD material it's the convenience of hooking it up to the TV more than anything else. "Upscaling" players fake an HD picture by blowing up the SD picture and processing it a bit to look better... but your TV can do that already. It has to convert the analog input to digital anyway.

With a DVD player, there isn't much of an advantage to using HDMI, 

but the entertainment industry ("Hollywood") is very powerful 

(they have a lot of $$$$$) and they instituted HDMI so that you and I 

could not make direct digital copies of their precious movies.  

The two types of connections give similar results with no major differences unless you are using a t.v. that gets better than 1080 i 

With an HDMI cable, your television will get digital high-definition video and audio transmission with a single wire, with a resolution until 1080p.

With component cables (red, blue, green), it will get analog high-definition video transmission, with a resolution until 1080i.

Besides better video and audio quality, it's far easier to hook up one connection than three or more.

Plus, more and more modern flatscreen TVs do not come with analog inputs anymore.

HDMI is digital and can transfer ultra high definition images whereas AV is analog and can only manage medium definition..