When you're eloquent, you have a way with words. An eloquent speaker expresses herself clearly and powerfully. Even though eloquent usually describes oral speech, it can also be used to describe powerful writing.
Being eloquent is about using words well. All the great writers from English class — such as Shakespeare, Mark Twain, Emily Dickinson, and Virginia Woolf — were eloquent. A great orator or speaker like Martin Luther King was eloquent. When something is beautifully, gorgeously, perfect said (or written), it's eloquent. Being eloquent requires your words to be smooth, clear, powerful, and interesting. To write or speak in an eloquent way takes a lot of work.