A baby grand piano (or just "baby grand") is the smallest of all the grand pianos. It has been classically defined as a grand piano that is between 4' and 5'8" in length. A concert grand or orchestral concert grand is over 8'11" in length.
As a result of its shorter length, the tone and power of the sound produced by a baby grand is remarkably inferior to its larger counterparts. The sound quality on a baby grand can often be less desirable than even a good upright piano (or vertical piano).
The smaller size also results in a much lower price for the baby grands. Good concert grand pianos can cost well over $60,000 which is cost prohibitive for many people purchasing their first piano.
Baby grands are usually more expensive than comparably sounding upright pianos, but they are often chosen for their aesthestic appeal.
You will often hear of even smaller "toy" or "miniature" pianos advertised as baby grand pianos. A "real" baby grand piano should have full sized keys and a full sized keyboard covering 7 1/2 octaves with 88 keys. Tiny pianos for children often have small keys and less than 30 keys (covering only 2 1/2 octaves). Many don't even have strings in them when you open them up, but instead have only metal bars or rods that resonate. These things might be acceptable teaching toys for children 2 to 4 years old (or any child that is not responsible enough to properly care for a piano), but they really shouldn't be called "baby grands".