1. NXX is most commonly used to refer to three-digit code that forms the second part of a 10-digit North American phone number (digits 4-6). This is also known as the "central office code" or "exchange".
Traditionally, in the age of competing phone companies, each NXX is assigned to one company. Because four digits follow the NXX, that means available phone numbers were originally assigned to phone companies in blocks of 10,000. However, more recently, NANPA has been breaking up NXX blocks into groups of 1,000 that can be assigned to different companies.
While a phone company may "own" a block of 10,000 or 1,000 numbers, number portability allows customers to re-assign their individual number to a different company.
See: Number Portability
2. "NXX" can also refer to the basic number format used for both NPA (area code) and NXX (exchange) numbers. N means 2-9, while X means 0-9. Therefore NXX simply means a three-digit number where the first digit can't be "0" or "1".