A linear-bounded automaton (LBA) is a type of Turing machine that operates within a limited amount of tape space. Specifically, the tape length is linearly proportional to the size of the input. This restriction allows LBAs to recognize a subset of context-sensitive languages, making them more powerful than finite automata but less powerful than unrestricted Turing machines. LBAs are important in the study of computational theory because they help define the boundaries of what can be computed with limited resources. They are used in various applications, including compiler design and formal language theory, to analyze and process complex languages efficiently.