The Wikipedia definition for public speaking is "the process and act of speaking or giving a lecture to a group of people in a structured, deliberate manner intended to inform, influence, or entertain a listening audience. Public speaking is commonly understood as face-to-face speaking between individuals and an audience for the purpose of communication. It is closely allied to "presenting", although the latter is more often associated with commercial activity. Most of the time, public speaking is to persuade the audience" ("Public Speaking").
Answers.com defines it as "the act or process of making a speech in public. You could also say it is the art of effective oral communication with an audience. The word "effective" implies that public speaking is much more than just talking at people. "Effective" means you are making a speech in a way that people understand and remember. To speak effectively, you need to define what you'll talk about, think about who will be in your audience (as it influences the tone and language of your speech), gather information, read and organize your research, choose tools to aid your delivery, prepare notes or a written copy of your speech, and practice the speech. The audience itself is generally defined as being more than one person. Additionally, although public speaking can be impromptu, it usually connotes a degree of structure and deliberateness to your delivery. ("A Definition of Public Speaking: Purpose, Need, and Development")