Words can be described as "vessels for thoughts". Our vocabulary affects the ways in which we are able to conceptualize the world around us. Or in other words, without a word for something we cannot think about something.
This linguistic relativity is expressed in the Sapir-Worf hypothesis that says that language influences (or determines) our thoughts.
An example can be found in the book of Genesis in the bible: In the beginning, the earth was without form and void. Only after God spoke the word, plants and animals took form.
Another example can be found in George Orwell's novel 1984: The government works on Newspeak, a language reform that removes all words related to freedom or rebellion from people's vocabulary - and therefore removing people's ability to think about concept such as freedom or rebellion.
Inventing new words allows us to think about new concepts. For example, medical researchers create new names for a set of symptoms. Giving these symptoms a name allows pharmaceutical companies to start research groups, and patients to form special interest groups.
The number of words in English has grown from 50,000 to 60,000 words in Old English to about a million today (source).
The RSAnimate video below illustrates a talk by psychologist Steven Pinker about language as a window into human nature.