Allow me to translate. “Yes, you can, to a point.”
Our “hot_fiat” of this parish is bob on. An email has a body which is the bit everyone looks at, and a hidden part which is a record of everywhere it’s been. When it arrives at a mail server, the server leaves its own mark as it passes it on. Email is basically the mucky woman of the IT world.
The hidden part is the “header” and will – well, should – contain IP addresses of its source, destination, and every other hop it’s taken en route. By looking at that header you can see where it came from, theoretically at least.
Faking or “spoofing” an email address is trivial, but spoofing details gets increasingly difficult the farther up the food chain you go.
If you’re using webmail rather than a traditional client then it’s a bit different in so far as you aren’t the origin of the email, the web server is. From the recipient’s point of view they won’t be able to tell where it’s originated from; however, the service provider will have web logs showing where the sender connected from.
Though, as Matthew Broderick once said, there’s ways around that.
(EDIT: sorry for repeating points made by others; the conversation moved on whilst I was typing that.)