The easiest way to think about words and how they can be added and subtracted like vectors is with an example. The most famous is the following: king – man + woman = queen. In other words, adding the vectors associated with the words king and woman while subtracting man is equal to the vector associated with queen. This describes a gender relationship. Another example is: paris – france + poland = warsaw. In this case, the vector difference between paris and france captures the concept of capital city.
It’s worth noting that one of the pioneers and driving forces in this field is Google and its machine translation team. These guys have found that a vector relationship that appear in English generally also works in Spanish, German, Vietnamese, and indeed all languages. That’s how Google does its machine translation. Essentially, it considers a sentence equivalent in two languages if its position in the vector spaces of each is the same. By this approach its traditional meaning is almost irrelevant.
Teodor Darabaneanu 