Samsung has region locked both the American and European models of the Note 3, allowing them to only work within limited areas by default. You can use the European version, largely all of Europe, while the American version includes North, Central, and South America, as well as the Caribbean.
The Note 3 can connect to foreign networks, it won't be able to do so simply through using a foreign network's SIM card. Note 3 owners will have to pay their local carrier's international roaming fees in order to tap into wireless networks on another continent.
Given that Samsung has been telling the world about the Note 3's wide support of LTE bands, the region lock is daft. It is locking up one of the features of the Note 3 and making it useless.