A person's vocabulary is basically the group of words they are most familiar with and choose to utilize. That is the most basic answer you can get for the question "What is vocabulary?". In order to answer that question in a more detailed and thorough manner, every aspect that comes with the term vocabulary must be explained. There are several different types of vocabularies. Speaking, writing, listening and reading are of the main types that people use on a daily basis. Each type are all important to the structure of vocabulary as a whole.
Speaking vocabulary is all of the words a person can use through speech. This is a very powerful type of vocabulary. Potent speakers, musicians, singers, poets etc... have the ability to influence and move their audience/listeners with their charisma and with how they utilize this type. People who are very strong and innovative with this type have the power to control their audience in how they perceive, think and act.
Writing vocabulary is all of the words a person can use when they are writing. This is another eminent vocabulary type. Like speakers, writers also have the power to influence many people with how they use their words. A lot of times, both writing and speaking vocabularies are combined and they can compliment each other very well. E.g. If a speech or poem is prepared in writing, the writing completely negates the need of having to think about what to say. All of the thinking was already done before hand and put into the form of what has been written.
Listening vocabulary is all of the words a person can recognize through listening. The larger this vocabulary type is, the easier it is to understand others who utilize speaking vocabulary. Listening plays a significant role in the overall growth of vocabulary since you can encounter new english words from several different sources simply through hearing or listening.
Reading vocabulary is all of the words a person can recognize via reading. This is very important for understanding content produced by those who frequently use writing vocabulary. Like Listening, reading also plays a significant role in the overall growth of vocabulary. It's very easy to learn new words while reading.
Aside from the above main vocabulary types, there is also focal vocabulary and vocabulary lists. Focal vocabulary is a group of words or terminology that pertains almost exclusively to one particular word or phrase. Those groups of words can be referred to as vocabulary lists. E.g. a list for the word "Pirate" would consist of words like, ahoy, matey and cutlass. The latter three words would be a part of the vocabulary list and "Pirate" would be the word that the list pertains to.
Vocabulary strengthens itself almost naturally. People encounter new words almost every day whether it be through hearing/listening to someone else say the word or through reading newspapers, books, blogs or articles etc... When someone encounters a word they don't know the meaning of while hearing/listening to someone speak and notifies the speaker that they don't know the definition of that word, it is explained to them. When encountering an unfamiliar word on the internet while reading something like an e-book, blog, discussion on a forum or an article, it is very easy to find out the definition of that word through dictionary sites. As long as people care enough to learn and are in an environment where new words are being used in literacy, speech, or music their level of vocabulary should perpetually increase. This invigorates each of your vocabulary types making it easier to be creative and charismatic with speaking and writing and to be more understanding and intuitive when listening and reading.