Netcat is a basic network tool for reading/writing TCP/UDP connections. In the example you gave, you are telling it to run the program specified by -e across TCP to the remote machine and port number. In that particular instance you were sending a bash shell to his machine, presumably where he had a netcat listener waiting.
Netcat is truly the swiss army knife of networking. You can do so much with it. You can:
- create proxies
- grab service banners
- port scan
- reverse shell
- bind shell
- use it as a simple web server
- transfer files across the internet
It is an immensely powerful tool.
To answer your question about whether or not he could use it to access your mac: Not it in itself. You had to initiate the reverse shell back to his box. Without you sending the shell, he could never connect. However, after connecting he would have been able to plant a backdoor for persistent access.
An attacker with any skill would have cleaned up his session (and system) logs, so you can't even trust those to tell the truth about what happened. The ONLY truly safe thing you can do is to wipe the box.