Nikaya is a word of Pali origin and Sanskrit usage which was adopted into English in reference to Buddhisttexts.
Regarding the Buddhist canon (the Sutta Pitaka in particular) the meaning of the term is equivalent to the English "volume" or "tome" -- although the works in question are so voluminous that few unabridged editions can fit an entire Nikaya into a single volume.
The word has other usages: we should note particularly that in the south-east Asian Theravada school it is the polite term for monastic orders, divisions among monks, or "sects".
An equivalent used in China is Agama, and the Sutta Pitaka of the Pali Canon is sometimes referred to as "the Agamas" by Mahayana Buddhists -- or as "the Nikayas" if they are in the company of Theravada Buddhists.
Nikāya Buddhism is a general term for those schools of Buddhism that accept only the nikayas and agamas—that is, the type of sūtras which are devided into Suttapitaka, Vinayapitaka and possibly an Abhidhammapitaka.
It is sensible to use a terms for a division of population which is ideally used by themselves, and failing that, at least not offensive to them.
The term 'NikayaBuddhism' is just a replacement of the term Hinayana, which keeps in place the tendency to regard the seperate early schools (and their differing ideologies) as one form or type of Buddhism.
NikayaBuddhism is a general term for those schools of Buddhism that accept only the class of sutras collected in the Pāli Canon as authentic.
NikayaBuddhism is distinguished from the Buddhism of the various Mahayana and Vajrayana schools, which accept the authenticity of a range of other scriptures.
Tradition states that the protagonists were two NikayaBuddhist groups: a conservative group known as Sthaviravada which insisted on strict observation of vinaya and a more liberal group known as Mahasangikas which argued that some minor rules could be relaxed.