I'll try to explain the ones I know:
Bagatelle - This is just what it means, a 'trifle'. Usually, it signifies a short piece without any considerable depth, unlike the larger forms.
Barcarolle - The name given to songs sang by gondoliers in Venice, Italy. Usually creates a water effect on the listener.
Bercuese - a lullaby, something that evokes sleepiness or resting. Chopin's Berceuse has a mesmerizing bass 'rocking' form while the melody moves through variants.
Etude - A study. A technical exercise for improving technique of the fingers of some sort. Although many are beautiful (i.e. Chopin, Scriabin) that is not a requirement.
Fantasie - A fantasy, a piece without any fixed form at all. IMO used to defy the normal rules of form and to bring more freedom to the music.
Fugue - A piece without any fixed form, except in the beginning. One voice must present the subject, and the others must, one at a time, answer it. This form usually has other parts that help keep the fugue subject from getting stale, such as stretto, diminution, augmentation, episodes, etc.
Mazurka - A Polish/Russian dance in 3/4 time, with the accent on the 2nd or 3rd beat.
Nocturne - A piece that evokes night scenes without any fixed form, like a miniature fantasie.
Prelude - A piece used to ready the ear for another piece that follows it. Can also be used as its own piece, standing by itself as in Chopin's and Rachmaninoff's preludes.
Polonaise - A Polish dance in 3/4 time with a specific beat: 8th-16th-16th-8th-8th-8th-8th note, usually in minuet-trio type form
Sonata - A piece of usually three to four movements (or segments, as in Scriabin, Liszt and Scarlatti) where all movements are bound by different themes, thereby keeping the entire sonata whole, but the different movements separate. They must be contrasting, but with things that bind them together.
Sonatine - A shorter sonata, sometimes an exercise
Suite - A set of dances, usually in the same key or similar keys, that portrays a theme used in a variety of ways, i.e. Bach's English Suites. The different dances usually have the same type of feeling to them, like sadness, happiness, or anger.
Waltz - A dance in 3/4 time usually reserved for the dance floor (i.e. not for recitals, except Chopin's of course). Its accent is on the first beat of each measure.
Remember, take everything I say with a grain of salt on these things. I hope I've at least been helpful.
Phil
Topic: Meanings Behind Peice Type's