The accepted answer is not strictly correct, although it addresses the most common usage in computer graphics. Aliasing is a fundamental concept in signal processing and the mathematical theory of it predates computer displays. It is also not really true that "it is a side effect of the fact that pixels are square". Aliasing exists any time you discretely sample a signal at a rate below the Nyquist rate for that signal and affects digital audio as well as images and many other types of discretely sampled signals. Aliasing in computer graphics is a side effect of discrete sampling, not of the shape of the pixels.
Anti-aliasing in computer graphics is a deep and complex topic and there's a lot more to it than just edge anti-aliasing. Again, there's a lot of underlying theory from signal processing and it's an active area of research in computer graphics how to anti-alias effectively, not just for edges but also for temporal aliasing, for aliasing when reconstructing a BRDF in pixel shaders, for shadow edges and in many other areas. Mip-mapping of textures in 3D graphics is a well established anti-aliasing technique that is addressing an important problem other than edge anti-aliasing for example.
It's really a mathematical phenomenon more than a physical one but it shows up in engineering in many areas other than computer graphics. I wouldn't really describe it as a numerical phenomenon either - it's a result of discrete sampling, not of the discrete representation of numerical values on a computer, although that can cause aliasing effects too. Understanding the fundamentals of signal processing is a good foundation for understanding how aliasing manifests in computer graphics and for understanding how to go about reducing it.