When people talk about a "big hitter," an idiomatic phrase in English language, they are referring to someone who is important, someone who is respected and has a good reputation within a particular field or community. This is just one of several idioms using the word “big” to generally mean important, associated with various positive adjectives like well-known or successful, or in command of many people and resources. This phrase seems to have come from an allegory to the sport of baseball, where a big hitter is a player who is known for hitting home runs or associated with strong performance.
In general, those who are referring to a person with a lot of power or importance may call that person a big hitter, a big fish, or a big cahuna. These are all idiomatic phrases with similar meanings. In calling someone a “big fish”, the speaker is often referring to a longer phrase “a big fish in a small pond” which is used to refer to someone at the top of their industry or at the forefront of their field, or again, someone with the most controlling interest in business, political power, or similar influence.
Using the phrase “a big hitter” is not the only way that English speakers can use idioms drawn from baseball. For example, someone might say that a person “hit it out of the park” if they were successful with a project. Alternately, they might call a successful project or proposal a “home run.” Someone who fails to close a deal may be said to have "stuck out." These figurative phrases are among the most common in the American business world.
Although many people think of the phrase “a big hitter” as related to baseball, some word historians argue that the phrase actually may have originated from the sport of boxing. Here, a heavy hitter would be a fighter who is able to hit hard and knock down an opponent. Some reference materials have linked this phrase to boxing and dated its origin in the 1900s.
Some linguists look at phrases like “big hitter” as a way of assessing the sociological relationships within a community, and how they are expressed through language. For instance, considering who gets the title “big hitter” and why they are so-called can reveal a lot about the values of a community. This kind of mixture of linguistics and sociology helps researchers to understand a society through its own voice, and to provide more definition of its distinctive features.