To amplify on the other answer, an "average person" with a little technical knowledge can trace the IP address to the ISP in seconds (the "ISP" could be a commercial Internet provider where the customer uses dialup/DSL/cable, or other entities providing Internet access such as a business, university, or public library). Getting "reverse DNS" tells you what the ISP is, and possibly the state or city where it originated. The ISP DOES keep records of which customer is on what IP address at every instant, but as Tsu implies, this is considered "privacy" info by all ISP's, and you need a court order (thus you need to explain to a judge a good reason why you would need this, such as the email containing a death threat) to get the ISP to tell you the customer name. And as Tsu says, if the customer uses an anonymizer or other IP-obfuscating process, it can be a lot harder to trace.
Googling reverse DNS, I just found this site:
http://remote.12dt.com/lookup.php
It showed my IP address in the textbox (as usually shown, four decimal numbers betwen 0 and 255, separated by three dots). I pressed lookup and it shows:
74.36.193.57 resolves to
"74-36-193-57.br1.frt.ga.frontiernet.net"
Top Level Domain: "frontiernet.net"
With that it's easy enough to figure out that my ISP is frontiernet.net, and the '.ga. part almost surely means I'm located in Greorgia.
Email headers have lots of IP addresses for all the mail servers they might go through, and spammers (I learned to read headers over ten years ago to track spammers) have often forged things and added fake headers to make things harder to trace, as well as using 'blind relays' and such. What's even worse, in more recent years, spammers use 'zombies' or infected online computers (maybe YOUR computer!) to send spam, so the IP address in the email headers point back to YOUR computer instead of theirs.
But for people without specialized technical knowledge sending such an email, they probably leave enough traces to out themselves. If the content of the email prompts you to make a list of people you suspect of sending it (perhaps it threatens your family members by name and you know who knows their names and who you would suspect of doing that), the IP address may give enough other information to pretty much tell who it is (say the IP address is from a certain college campus, and exactly one person on your list is a student or employee at that college). That's not enough by itself to convict anyone in a court of law, but it's enough to get a court order for the IP address and date/time the email was sent, the college's IT department will tell who was logged on to the computer at that IP address, and then THAT will be enough for a conviction.
I was on the SPAM-L list years ago and saw this happen a lot to spammers (though not nearly often enough, for the amount of spam sent out!). Hope this wasn't too much more than you wanted to know...