Eigen is the bread and butter of numerical computation in C++, just like how Numpy is the bread and butter of numerical computation in Python. It is the only (widely used) math library that can optimize its expressions in compile-time (example: A + B + C actually fuses the additions together rather than creating temporary vectors/matrices) As a result it gets competitive results with more conventional BLAS or specialized libraries while being much more ergonomic to use. (You can opt to use a BLAS backend with it though, performance can depend heavily on your specific usecase).
Tensorflow is using it in their CPU backend (which is the reason why there are some Google engineers participating in its development). Its usage is also prevalent among many different disciplines including machine learning, optimization, physical simulation, graphics, geometry processing, you name it.