What does it mean by "ever since"?

It just means 'since'. Its generally used in sentences that don't have years or time explanations.
Example-

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.

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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

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Ever since

from the end of an event or time frame to the present