dear dread fish ,
From what I understand, when they talk of a person being an emanation of a "deity" it means they embody the attributes of that deity. The deities represent aspects of enlightened mind, and the Dalai Lama certainly is very compassionate.
excuse me I used the term emination (meaning to manifest)
it is a subtle understanding , one often played down by the present dalai lama , however it was allways commonly accepted that the dalai lama is an embodiment of chenreizig , not just the atributes of chenreizig .
I have just finished reading a biography of the 13th dalai lama written just after his death , relating many conversations with the 13th during his reign and explaining the beleif of the tibetan people as to the divine nature of the succession of dalai lamas
I canot quote the entire chapter relating to the nature of the dalai lama , but will quote a small section ,
....."it will be seen that the 13th dalai lama whos life is portrayed , allso fulfilled the triple role of preist , god and king . ....
....there are indeed others who like the dalai lama , have set aside the privilage of
"passing beyond sorrow ", and have concented to be born again in order to help on the upward path all beings , men , women , birds , beasts , fishes and insects , infact every kind of
"mind possessor". such a one is known as a
"trul ku " i.e. "a phantom body ". these are lamas in whom the emination from some deity or byegone saint is present in an ocult manner ."
I hope this gives some indication of the true nature which were attributed to the dalai lamas , I would stress the use of the the wording "present in an ocult manner"
if earlier writings are studied it is possible to see the attitude of reverence held by the tibetans , towards the dalai lamas and any other eminations including the regents the panchen lamas and other high lamas , but in the light of the excile of the tibetan government and the 14th dalai lama there has been a distinct change in the emphasis from tenzin gyatso himself who is remarkably humble and for reasons of insight into the delicate position as regards to tibetan buddhism ,therefore he has chosen to teach according to the situation .
hope that explains a little ,