Yes and no.
Yes it can be traced to your ISP, ergo to the geographical area in which your ISP exists. This is more often that not where you live. But no, it can't be easily and directly traced to you.
It is required by law to provide correct information when reserving Internet resources (domain names, IP addresses), those information are stored in a publicly accessible WHOIS database. Since your ISP is the one who reserved a stack of IP addresses, they usually are linked to it. If you are assigned an IP address dynamically and you lookup your IP address in WHOIS database, it leads to your ISP.
When the authorities want to trace you even more (beyond just the ISP level) they simply provide a legal request (such as subpoena) to your ISP with the time of your activity. Your ISP simply looks up their database and see who was given that IP address at the that time. After they know it's you, they simply hand over your registration information (Full name, address, etc.).
In the case of static IP addresses, things are a little bit different. Depending on the jurisdiction and possibly your ISP policies, your statically assigned IP address maybe linked directly to your identity and thus can be looked up in a WHOIS database. Some ISPs provide a domain-privacy-like service for your static IP, in which they keep the IP publicly linked directly to them. Again, in this case, a legal request can be filed and the ISP will hand out your real information.
In your question you mentioned something about connecting to WiFi again and getting a new IP address. Even though you're getting a new local IP address, your public IP address is still the same. That's because almost all home routers and WiFi access points create a NAT by which they separate your home network from the outside world, and no matter what IP address you have inside the local network, the world still sees the same public IP address.