What is an academic sabbatical?
The definition of sabbatical in Wikipedia refers to labor terminology rather than academic sabbatical leave. As a privilege to employees, they can have temporary unpaid leave (for any personal reason) without losing their job.

However, academic sabbatical historically is somehow different. When a scholar needs peace of mind to focus on a challenging issue, s/he will visit a new institute to experience a new atmosphere. While still being in the academic environment, not having heavy official duties.

There are several motivations for a sabbatical leave (at least as I have seen):


A manager finishes an administrative position (e.g. Dean), and wishes to rest in a different atmosphere, but not far from academia.
A researcher working on a new idea, prefers to focus on his/her work somewhere with less commitments on everyday responsibilities (e.g. teaching, advising, etc).
A researcher is exploring new possibilities and opportunities, spend some time in a new department to live with new colleagues for a while.
A researcher is collaborating with another group and spend a year in the host research group as a visiting scientist/professor while being on sabbatical leave from his/her institute.
A professor in a mid-level university finds a temporary position in a top university. This is the base for many visiting professors in the US universities, e.g. international professors can experience working in the US universities. Even there are associate/assistant professors who find a post-doc position in the top universities, and use sabbatical leave, not to lose their job at home.


In any case, sabbatical allowance mainly depends on the university employment rules.