Any dog owner will tell you that dogs understand many words, and studies support this impression. In addition to dogs with regular, “family dog” knowledge levels are dogs with an extraordinary level of word comprehension. These dogs have been called “gifted word learners” and they appear idiosyncratically across countries, breeds, and households. Dror et al. examined the ability of these dogs to pick up words through conversations not directed at them. Using an approach designed to study understanding in toddlers, they found that the dogs were able learn words through overhearing just like, or even better than, 1.5-year-old children. —Sacha Vignieri [Editor]
From abstract:
... In this study, we demonstrated that a small group of Gifted Word Learner dogs, which possess an extensive vocabulary of object labels, can learn new labels by overhearing their owners’ interactions. Moreover, we show that these dogs can acquire novel object-label mappings even when the labels and objects are not presented simultaneously. Taken together, these results suggest that Gifted Word Learner dogs possess sociocognitive skills functionally parallel to those of 18-month-old children.
Note that this is only for what the authors described as a subset of "gifted dogs": "Although dogs readily learn action labels (23), to date, behavioral evidence of learning object labels were documented in only a small group of dogs (24). We previously defined this small group as Gifted Word Learner dogs..."
The full article seems to be behind paywall/institutional access. If anyone finds a full-text link please definitely share here