Someone connecting to your local network: Very likely.
Someone breaking into your computer: Prety unlikely.
Your local network is probably NOT secure, making it open to anyone.
The only content on your computer that can be accessed is that contained in any explicitely shared folder. An explicitely shared folder is one that YOU have set as a shared folder, like my music to be able to play some music from another device on your network.
All routers come with a factory set default password. That default password MUST be changed at the first oportunity!
Enter your router's configuration page. You can try connecting to http://192.168.0.1/ (a very common local router address) or the address provided by the user documentation.
That documentation also contain the default password that you'll need to use.
If you used the provided setup application/wizard, you probably had been invited to enter a new network name and main password.
EXTREMELY important!
CHANGE the main password from the default one.
It's also an idea to change the local network name.
If the person connecting is just connecting and not hostile, he probably did not bother changing the main password.
If you don't need wireless and use only cabled connection, you should disable wireless (wi-fi).
If you use wireless:
Set a good passphrase. At least two "words" using lower and uper case letters, numbers and any available special characters.
You can go to https://passfault.appspot.com/password_strength.html#menu to test your passwords or passphrases. You need a "Time to crack" longer than a century using those options:
$180000 password attacker and Microsoft Windows system.
Enable the strongest encryption and autentification possible.
Without that, anybody in the area can connect wirelessly to your network.
If you have any device that don't support strong autentification and encryption, those must be restricted to cabled connection ONLY. Otherwise, they prevent the use of strong autentification and encryption for ALL devices.
NEVER EVER use beacon suppressing!
It forces your computer to anounce itself, including the network name, it's identity and PASSWORD in clear.
The call looks like (very similar to an e-mail address)
"computer_name.password AT network_name".
The call is sent every 20 seconds.
It alow someone to masquarade itself as your computer when you are not connected. It also allow anyone to imitate your network and trick your computer to connect to that fake network.
Electro
December 2013