Emma

Cae-mi-ilia = "bright my sun"
Ilios = ilia = sun.

Brought to England by the Normans; short form of compound given names beginning with a Frankish prototheme Ermin- or Irmin- "entire", from Proto-Germanic *ermunaz.

The name was popular at the beginning of the century, was forgotten for several decades, and now it's very popular yet again. I wonder what's next...

This name also means "grandmother" in Greek.

Emma means 'blood' in Greek.

This is actually a variant of Emmanuel, which means "God with us". There's more to it than just "ermen". (Some random atheist probably reported that and got it removed.)

A famous bearer from history is Hemma of Mělník (b. before 950, d. 1005/1006) was the wife of Boleslav II of Bohemia and a Bohemian Duchess.

Please, understand, Emma is NOT the feminine of Emmanuel!

This name is a shortened version of the German name Ermintrude. The name Emma isn't a pet name of Emily, if anything it would be the other way round. Emma is more of a classic name than Emily. Emma is far prettier, because of its sound (eh-ma) than Emily (em-i-lee), and also its sound (of how grown up it sounds). Emily (as another person pointed out) is more of a child name.

I had always thought that Emma was a short form of Emmanuella or Emmanuelle.

According to Patrick Hanks and Flavia Hodges in "Dictionary of First Names" Oxford University Press (1993)
Emma - (f.) English: of Germanic orgin, introduced to Britain by the Normans. It was the name of the mother of Edward the Confessor. It originated as a short form of the medieval versions of compound names such as ERMINTRUDE and IRMGARD, containing the element of ERM(EN), IRM(EN) entire (cf. IRMA). It is now sometimes used as a pet form of EMILY, but this is etymologically unjustified.

Emma is of English origin. It means energetic.