The term "literary movement" simply refers to a period of time in which many authors followed similar patterns of writing or used similar subjects or approaches. Literary movements frequently were shaped by contemporary events and influences upon the authors whose names became associated with a particular movement. The actual naming of a "literary movement" as such often did not occur until years later, when readers could look back and recognize the similarities between authors and written works.
Some examples of literary movements could include Romanticism, which developed as a reaction to the Enlightenment in Europe and includes Victor Hugo and Lord Byron among its authors; American Romanticism, which emphasized influences from American history and is exemplified by works of Nathaniel Hawthorne and Washington Irving; and Transcendentalism, in which Ralph Waldo Emerson and Henry David Thoreau advocated individual freedom from technology.
A literary movement is a general term for pieces of literature by different authors (usually over the same time period) who share a similar impetus for writing in some way. Usually these authors are considered part of a "movement" because they have similar ideas about something.
These terms, helpful for curricula or anthologies, evolved over time to group certain writers who are often loosely related.
Note the quotation above which indicates the literary movement titles are more important for learning in a future time than they are for the actual writers writing within them. Still, the selections of works from this literary movement might have similar content, thought, form, style, or philosophy.
Please realize that scholars are continually debating the dates and even the "titles" of literary movements. The answers to these questions are not cut and dry. For example, sometimes a literary movement is simply created to counter another. For example, the beautiful nature-driven philosophy of Transcendentalists like Thoreau (who wrote the very philosophical work about simplicity and solitude called Walden) was countered by the destruction of nature found in the Anti-Transcendentalists like Melville (such as in his famous novel, Moby Dick).
Even though the dates and "titles" are debated, they do have to congeal in the same general time in history. Because of this, the literary movement of a time period is often influenced by the historical happenings (and politics) of a time. For example, look at the intense Classicism espoused by the writers before and during the Revolutionary War. Further, the emotional and nature-loving Romantics correspond with the writers during and after the French Revolution.
If you look up "literary movements" on wikipedia, you will find a substandard list of only modern movements. This is why it's important to have scholarly websites such as eNotes that can help you with nuances. But what we can clean from years of study is that a literary movement generally isn't considered "modern" unless it happens after the Renaissance, and that modernism is a very general term for hundreds of mini-movements such as absurdism and surrealism.
There are also movements within movements. Modernism (approximately late 19th century - the 1960s) contains many similar and/or different movements: Magical Realism, Surrealism, Futurism, Imagism, and Theatre of the Absurd - to name a few.