Misr indeed is an Arabic name for the region of Egypt, hence the frequent translation as Egyptian girl.
The tune, converted to a dance by the Greeks, is known in Arabic, Jewish, Sephardic Spanish and other languages of the Mediterranean area, but its exact place of origin, age and original intent of the name Misirlu (Misirli, Misrli, etc.) is not exactly clear.

The MIT Folk Dance Club Songbook, courtesy of a Brandeis Univ. web posting, has a translation of the transliterated Greek words, posted far above (first line Misirlu mu i glika su i matya). Extremely bad translation, but mostly understandable:

Miserlu, your sweet glance
has lit a flame in my heart.
akh yakhabibi, akh ya leleli, akh,
Your lips trickle of honey, oyme!

Ah, Miserlu, magical, enchanting beauty!

Craze will come to me, I can endure no longer,
Akh! that I might steal you from Arabia.

My Miserlu, crazy, black-eyed,
One of your kisses lights a flame in me.
Akh yakhabibi, one little kiss
From your sweet mouth, oyme!

Ah, Miserlu, magical, enchanting beauty!

Craze will come to me, I can endure no longer.
Akh! that I might steal you from Arabia!

www.cs.brandeis.edu/~ira/sb/fd.pdf
Folkdance