It just means 'since'. Its generally used in sentences that don't have years or time explanations.
Since 1995 I have lived in Chicago.
Ever since I left I have missed New York.
Ever since my aunt died I have been sad.
Edit- you can also use 'since then' if you are not explaining the time or specific event----
Since then I have been very happy.
Since I cut my hair I have been very happy.
It means "continually following"...
Ever since the surgery, I have had a pain under my arm.
Continually following the surgery, I have had a pain under my arm.
ever = continually
since = following
from the end of an event or time frame to the present