I received my political asylum 11 years ago, filed for Adjustment of
status 4 years and 4 months ago. My case has
been approved 3 days ago. 
The law says that "An applicant must have been lawfully admitted to
the United States for permanent residence. Lawfully admitted for
permanent residence means
having been legally accorded the privilege of residing permanently in
the United States as an immigrant in accordance with the immigration
laws."
What does this mean "lawfully admitted to the United States for
permanent residence"? When can I apply for citizenship???

I'm not a lawyer, but I was a refugee myself, so here're my two cents:

As a refugee, you should have received the I-94 "white card" with INS
number (A-.....) when you immigrated to US. The INS stamp on the I-94
said that you can permanently reside in the US.  The date of the I-94
is the date when you were "lawfully admitted to the United States for
permanent residence".  Generally, you can apply for the citizenship in
5 years after that date.

In my case, I immigrated as a refugee in 1999; in 2002 I got a "green
card".  In 2005 I applied for citizenship and was approved.  I could
have done it in 2004 - five years after the date of entry.

Hope it helps.

Just a personal comment for both of you.  My congratulations for
escaping whatever horrors you escaped. In my very limited experience,
people like you make the  best citizens.  Thank you for making this
nation what it should be.  Hugs!