In case of numerical analysis, the Lagrange polynomials are suitable for finding the polynomial interpolation. For a set of specific data points with no two values equal, the Lagrange polynomial would be the lowest degree that or the corresponding values where functions coincide each other.
The interpolation polynomial for the lowest degree is unique and this is possible to find the solutions through multiple ways. The Lagrange Polynomial is perhaps the most suitable technique to reach that unique interpolating polynomial.
The concept was proposed in 1795 and first discovered in 1779 by Edwin. After this a consequence of formulas were published in 1783 by Euler mathematician. The popular usage of Lagrange Polynomials includes the Newton-Cotes method to find the numerical integration or secret scheme in cryptography. It is used to check the patterns in large oscillations that changes points that needs interpolation. In few cases, this is easy to use Newton Polynomials instead.
The Lagrange Interpolation polynomial was proposed to check the uniqueness of the interpolation polynomial and it is preferred in proofs or theoretical arguments too. Uniqueness can also ne defined as the invertibility of a matrix or a determinant. If you are still confused then Lagrange basis needs to be calculated again.
There are practical uses of Lagrange interpolation polynomials too like finding equally spaced points, oscillations, population behavior and more. This is not easy understanding the concept with this simple discussion but practicing them regularly will give you a better understanding of the topic.