Consider a simple cube under some given loads. The cube is composed of an infinite number of particles and each particle can translate or rotate in the 3D space. So theoretically this cube has an infinite number of degrees of freedom. The Finite Element Analysis method divides the cube into smaller chunks called elements and the corners of the elements are called nodes. Each node has a fixed number of degrees of freedom. So now the problem is converted from one having an infinite degrees of freedom to finite degrees of freedom. According to the laws of physics, under a given set of loads, a body always deforms such that it stores the least amount of energy possible. So the Finite Element Method finds the displacements of the finite number of nodes such that the energy stored by the deformed configuration is minimized. Based on the displacement values, other quantities such as strain, stress etc. can be calculated.
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