Lama, which translates as "superior one," is a title officially extended only to the few dozen Tibetan Buddhist monks who have achieved the highest level of spiritual development.
Most lamas are believed to be reincarnations of previous holy men, and their places in the hierarchy are determined by these identities. Tibetan Buddhism is divided into branches. The Dalai Lama and Panchen Lama lead the largest sect, and the Karmapa Lama heads the second largest.
The Dalai Lama is Tibet's spiritual leader, he holds the highest position within the dominant Gelugpa sect.
The Panchen Lama is the next highest Gelugpa leader,but does not have civil authority. When the Dalai Lama fled Tibet, the Chinese government tried to elevate the Panchen Lama to take his place. It didn't really work.
The Karmapa Lama is the leader of the Karmapa sect of Tibetan Buddhism. The current Karmapa, a 14-year-old boy , is the 17th incarnation and is the only high lama accepted by both China and the Dalai Lama. A few months ago the Karmapa Lama fled Tibet and is currently seeking asylum in India.
Source: Slate.com, DalaiLama.com, Karmapa.org