First Term, Long Answer

The very first term in the Technical Manual and Dictionary of Classical Ballet (from now on will be referred as "Ballet Dictionary") is ABSTRACT BALLET.  It is defined as "A ballet without a plot.  A composition of pure dance movement expressed for its own sake."

After doing some more research, I found the book Ballet 101:  A Complete Guide To Learning and Loving The Ballet by Robert Greskovic (pages 197-201, and 523).  He states that Abstract Ballet is a 20th century term for a ballet without a particular story or narrative.  These are ballets not driven by a specific plot-line containing ballet pantomimes, but inspired by the music or the movement itself.

The first Abstract Ballet mentioned was "Chopiniana" from 1907.  This ballet was based on the musical themes of Chopin.  Its original choreography was by Michel Fokine, and it was orchestrated by Alexander Glazunov.  In 1907 it was reworked and became known as "Les Sylphides".  It was different than the ballets that audiences were used to.  They no longer had to sit and wait through a narrative to get to the dramatic reason to enjoy the dance.  Since the holiday's are over, the "Nutcracker Ballet" came into my mind.  The beginning of the performance largely contains pantomime and there is a large section of Act-1 that the viewer has to watch until the dream sequence starts and then the ballet world can begin.  As a child I thought the first part of this ballet was long (and I hate to say boring).  As an adult I can now appreciate the ballet as a whole, but understand why choreographers may have wanted to break away from the typical outline of a ballet.

From the technical side of things, Abstract Ballets are more commonly found in 1-act length rather than the multi-act Grand Ballets that came before them.  This was because they didn't need to "set up" the ballet sequences, but could just jump right into them.  The music became much more important being the inspiration more than the accompaniment.  Composers even got higher billing on the programs.  Also the costuming changed from the "old" ballets to the "new" ones.  Dancers were commonly found in simply a leotard and tights or a unitard so that the lines of their bodies could be seen better.

Some famous Abstract Ballets are:
--"The Four Seasons" choreographed by Jerome Robbins and premiered in 1979, to excerpts from Giuseppe Verdi's "I Vespri Siciliani" (1855).
--"Apollo" choreographed by George Balanchine and premiered in 1928, to two tableaux's composed by Igor Stravinsky.
--"Serenade" choreographed by George Balanchine and premiered in 1934, to Tschaikovsky's "Serenade for Strings in C" (1880).

I will leave you all with a quote from George Balanchine regarding Abstract Ballets:
"How much story do you want," he wondered.  "You put a man and woman on a stage together, and already it's a story."