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Academic tenure - The most well-known use. A professor granted tenure at a university has permanent employment and can only be dismissed for serious cause (misconduct, financial exigency, etc.). It protects academic freedom - the ability to teach and research without fear of losing one's job over unpopular ideas.
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General employment - "Tenure" can simply mean the length of time someone has held a job. ("Her tenure as CEO lasted 10 years.")
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Land/property tenure - A legal term describing how land is owned or occupied. "Land tenure" refers to the rights and conditions under which someone holds property.
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Public office - Politicians or officials may serve a fixed "tenure" in office, meaning the term or duration of their appointment.