Remember the days when connecting your turntable, 8-track, and tape player all used the same two cables? For years connecting audio to a receiver was a snap because there was only one way to do it. Well... those days are gone. Digital technologies have expanded the number of different connections capable of carrying audio to a receiver. While many devices are fairly self-explanatory, DVD players can boggle a consumers mind by offering, in come cases, five or more different choices to connect to a receiver. 
Analog multi-channel out can provide higher audio fidelity than digital connections in certain systems. Digital signals must be decoded at one end or another. If a digital connection is used, the receiver must be capable of decoding the desired signal. Analog connections are decoded in the player. 
Some DVD players are capable of sending a digital audio and video down one HDMI cable. There may be some high-end receivers that switch HDMI and pull audio at the receiver before passing video to the TV, but HDMI cables will normally be plugged into a television. HDMI enabled TVs will provide an optical or coaxial digital connection that will carry the audio to a home theater receiver. For surround sound users, this connection is not currently an end-to-end solution. 
Coaxial and optical digital connections are the most common connection used to transfer audio to a digital capable receiver. Most digital capable receivers should support both of these connection types, though some DVD players only have one or the other.
Stereo connections should be used on equipment lacking digital capabilities. Though one exception is DVD players that contain an HDCD decoder, which can give compatible CDs a boost in audio quality. However, a digital connection should still be made for movie listening.