should I turn on firewall

When you are at home, most home routers block unsolicited network connections. So only connections you intentionally setup would be allowed into your home, so unless you are that kind of geeky person that plays with router port forwarding, there is not a lot of work for a firewall to do, when you are at home.

What are you expecting it to do?

The reason for asking is that it's not a yes or no sort of question. Lacking additional details no one can answer it for you.

The default setting is "off" which is what it should be, except for certain circumstances such as BobHarris explained.