Language is unique to humans - other animals just "communicate". A recent theory to explain why homo sapiens survived and homo neanderthalensis did not, postulates that Neanderthal man never developed advanced language and was always at a disadvantage when competing with modern man.
I won't try to improve on Ray's answer, which seems to have it all covered, but I have a couple of thoughts.
Dr Konrad Lorenz, a world authority on animal behaviour, and the author of King Solomon's Ring, taught his cockatoo to speak. He knew that it was only repeating the words it had been taught without knowing that they had meaning. He said that only once did the bird ever say anything meaningful; when a tradesman approached the house the bird called, "Here's that man again." Lorenz put it down to coincidence and was almost certainly right.
My dog can talk but she doesn't use English. She taught me to speak Canine. Now I understand the words for I'm hungry, and Open the door, and I want to go for a walk, and a few other important basic phrases.
When statistically graphed, the human speech pattern makes a pretty clean 45 degree angle. So far, this unique pattern has been found in only one animal, the dolphin. Dolphins also pass the mirror test where a dot is placed on the dolphin and shown themselves in a mirror. They pass the self awareness test by recognizing themselves in the mirror and noticing the dot as new.
It's intriguing. I don't know if dolphins can "talk" to each other like we do. Scientists don't know either. We obviously have yet to translate a dolphin conversation :) but one thing that is proven is that dolphins are very intelligent.
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