It's obvious that people can communicate with dogs. Throw a ball and tell a dog "fetch," and the dog retrieves the ball. But do dogs understand the word "fetch," or do they just understand that you threw a ball and made a sound? They could also be focused on some other cue entirely — the tone of your voice, or the direction of your gaze. Luckily, scientists have looked into this.
A recent study in Frontiers in Neuroscience is interested in exactly this question. Can dogs understand words? "Understanding" is a big, complex concept — difficult to test in the scope of one study, and difficult to define for a dog. Think of all the things that go on in your mind when you hear a word you "understand": you remember what it means; if it has multiple meanings, you figure out which one makes the most sense in context; you grasp its tone and level of formality; and so on.