Although there are differences (some would argue important differences) in the details, the vocal tracts of other mammals are fundamentally similar to those of humans. Some mammals are able to use these similarities to mimic human voices. An example is "Hoover the talking seal", an orphaned harbour seal who was raised by a fisherman and started mimicking the sound of the burly voice of his adoptive father. Hoover's "speech" (sound sample below) is somewhat slurred, but the words "come over here" and "hurry" are nevertheless clearly audible.
Another rather endearing example of a "speaking mammal" can be seen on the next page, which features "Mishka the talking dog".
One reason why we find such examples striking is that they are rather unusual, and even the most gifted talking seal or dog would struggle to keep up a meaningful conversation for any length of time. How much we can learn about human speech from studying animal vocalizations is a hotly debated and controversial topic.