"With Liszt and Wagner, motivic transformation became a shaping force in music.鈥?Can anyone explain this?

I think what the statement is getting at is the transition in musical style that occurred with the end of the Classical era, and the beginning of the Romantic era. Mozart would be an example of a Classical composer. His work is characterized by melody, something called "gallant" style.

Liszt was an early composer of the Romantic era, but better examples are Chopin and Mendelssohn, with Beethoven's music really straddling the two periods.

Anyway, one important characteristic of Romantic era music is that they'll take a simple theme, maybe only a few notes, and play with it over and over, transforming it in various ways. They might play it backwards, or upside down, or double the time. The old masters did the same thing of course - all of Bach's works do it, but the difference is that if Bach was doing this in a fugue, he was following the strict rules of fugue. In the Romantic era, they didn't have rules, other than making beautiful music. So, variation was a tool for them, while it had been more of a path for Bach.

A great example of this from Liszt is Liebestr盲ume. If you listen carefully, you'll hear the melody repeated and transformed throughout the piece.

So anyway, a motif is just a series of notes. A transformation is a musical device that lets the composer reuse the motif and keep it interesting. So the sentence you quoted is saying that during Liszt and Wagner's lives, this device became the shaping force in music. We call that the Romantic era.

Think of a motive as a small melodic or rhythmic idea. Composers use motives (or these basic ideas) to create longer phrashes or themes in their music. Then they arrange, rearrange, transpose, sequence, truncate, elongate, etc etc ..basically perform many diff. functions on these motives and themes to create a cohesive piece of music. Throughout musical history different (more) types of functions were tried and tested and basically Liszt and Wagner became masters at taking their motive and themes and reworking them in different ways. It can be an amazing thing to listen to a piece of music...get to know an established melody...and then minutes later hear it return in an exciting an fresh (sometimes ingenius!) new way. This is what Liszt and Wagner did and their compositional styles have changed music and continue to inspire composers of today.

Definition of Motive: http://en.wikipedia.org/wiki/Motif_(musi...

EDIT: motivic transformation is not to be confused with the term "leitmotif". Leitmotif is defined here:http://en.wikipedia.org/wiki/Leitmotif

I'm not sure what you mean by "motivic". Wagner was the originator of the term "leif motive" or motief.
By this, he meant an individual musical signature for a specific character, emotion or object: some of the characters in his operas(he termed them music-drama)had an identifying melody assigned to them, or musical theme.
Brunnhilde is identified by a particular melody throughout "The Ring"; so that whenever she is the focus, even when she is not on stage, her "leif moteif" is played in the orchestra; or when the horde of Nibelungs is the focus, their banging away on their anvils is heard.
I'm not aware that Liszt is associated with the concept of motive, if that's what you were referencing. Your question is not really very clear. Hope this helps.

Wotan

For start, it is "leitmotiv", not 'leif motiv".
Wagner's leitmotiv has been explained to you. In Liszt's creation, it's about the same thing. The difference between Liszt and Wagner it's in the purpose of their creation: while Wagner wrote opera music (despite the fact he has a few very valuable instrumental pieces), Liszt has developed the instrumental music (piano music, orchestra music and piano with orchestra music) in about the same manner Wagner did it in the opera.
They both have the same aesthetic view: creating a work in which the main musical motive is presented in many ways (continuous series of leitmotivic variation in Liszt's creation and building an entire opera from a few musical motives, which are representing characters, images etc.).
Of course that the stylistic approach to Wagner and Liszt has much more aspects than that, but in the "motivic domain", basically that is the answer.