An interjection or exclamation of surprise.
This little term derived in the USA as a euphemistic shorthand for Jesus; in other words it is a minced oath. That original meaning is largely forgotten by those who use it now, who are in any account fewer than before, as it is now sounds rather old-fashioned. The further shortening of simple gee is still widely used in the USA, although neither version was ever common elsewhere.
'Gee whiz' - it doesn't sound like a euphemism, but it is.
The first record of it appearing in print is from Cody and Arlington's Life on the Border, 1876:
"Gee-wees!...I'll bet one hundred dollars on that hand!"
The currently accepted spelling was used soon afterwards; for example, this piece of doggerel from the Pennsylvania newspaper The Warren Ledger, 1883:
When younger days have flown
And we are older grown,
We sit and muse -
We've got the blues.
Morning and night we fret,
And, cold or dry or wet.
In petulance pout -
We've got the gout.
We have accomplished naught,
Our fight was poorly fought -