It is a computational model used to solve several problems in engineering. It is a numerical method that allows for discretisation of a partial differential equation and is hence one example of what is known as a "computer experiment" or a "simulation experiemnt".
It must be noted that while Finite Element Analysis is primarily taught in Mathematics and Mechanical Engineering courses, it's applications are broad, interdisciplinary and at the end of the day helps in forming computational simulations.
https://en.wikipedia.org/wiki/Finite_element_method
A good foundation in Linear Algebra : MIT OCW 18.06
Basics for numerically computing solutions of Partial Differential Equations : Lecs 37-40 of NPTEL Computational Techniques
A good background in C++ : Derek Banas series on YouTube
Coursera course on Finite Element Methods for Problems in Physics
Reference : NPTEL FEA Course