Zanjutsu or Swordsmanship (斬術, zanjutsu; Viz "Art of the Sword"; Cutting Technique) is the style of fighting that most Shinigami use. As the name would suggest it involved the use of ones Zanpakutō and their various different abilities to defeat an opponent. In addition to it's basic form, a Zanpakutō will have 2 other forms from which it can take. One being the Shikai ((始解, Initial Release) and the other being Bankai (卍解, Final Release). These forms can unlock the potential power of it and it's wielder.
Just like Shinigami, Arrancar also have a Zanpakutō of sorts, and therefore also use this technique, or one very similar. Like a normal Zanpakutō it has a different form to that of it's basic one, however it only consists of one stage as opposed to the Shinigami's two. This is called the Resurrección, which unlocks their sealed Hollow powers and form of the user.