MATLAB stands for Matrix Laboratory. MathWorks developed MATLAB as a multi-paradigm numerical computing environment and proprietary programming language. It has evolved significantly over the years to become a tool utilized by engineers, scientists, and mathematicians for various tasks, including matrix calculations, developing algorithms, data analysis, and visualization. MATLAB's applications span various industries and disciplines. It's used in image and signal processing, communications, control systems design, test and measurement, financial modeling and analysis, and computational biology. More specifically, in the academic world, it's a standard tool for teaching and research in mathematics, engineering, and science. Its key components include:

1. MATLAB language: A high-level matrix or array language with control flow statements, functions, data structures, input/output, and object-oriented programming features.
2. MATLAB working environment: This consists of tools and facilities for managing the workspace variables and importing and exporting data. It also includes tools to develop, manage, debug, and profile MATLAB files.
3. Handle Graphics: The MATLAB graphics system involves high-level commands for 2D and 3D data visualization, image processing, animation, and presentation graphics.
4. Mathematical Function Library: This is a vast computational algorithm library containing elementary functions like sum, sine, and cosine, complex arithmetic, and more sophisticated functions such as matrix inverse, matrix eigenvalues, Bessel functions, and fast Fourier transforms.
5. MATLAB API (Application Program Interface): This allows users to write programs that interact with MATLAB.

Its advantages include its ease of use, application versatility, availability of numerous toolboxes for specific applications, and a vast community of users and contributors. In contrast, its disadvantages include its cost, as it is proprietary software, potential performance issues for large-scale computational tasks, and the fact that it might not be the best tool for every programming or data analysis task.