A Kilobyte is a data size unit, used with relation to data storage and processing, as well as data transmission.
The number of 1024 bytes for a kilobyte is a result of the binary nature of the bits and bytes (bytes are usually represented in hexadecimal numbers, but still stand for basic binary values). The base 2 to the power of 10 equals 1024, so that is the correct value of a kilobyte is 1024 bytes (in contrast to the decimal system, where "kilo" means 1000).
And with each byte being made up of 8 bits, a kilobyte is equal to (8 x 1024) = 8192 bits.
See the page about bytes for more detailed information.