What is an academic sabbatical? The Wikipedia definition of sabbatical doesn't match how I think of an academic sabbatical. What does it mean to go on academic sabbatical, and does it depend on the country?
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.