Principal Component Analysis (PCA) is the identification of linear combinations of the variables which account for certain proportions of the variance of the set of variables. The selection is based on the eigenvalues of the dispersion matrix of the variables. At the end of the day the chosen factors are much fewer than the original variables. The first principal component is associated with the largest eigenvalue and therefore the highest amount of the variance. The second principal component is associated with the second largest eigenvalue and ir associated with most of the remaining variance, and so on. Typically, the first few principal components account for virtually all of the variance. The principal components are uncorrelated with one another. PCA literature is in most multivariate analysis text books. A software is minitab is very good for PCA.
The discussion on stackexchange might help: https://stats.stackexchange.com/questions/2691/making-sense-of-principal-component-analysis-eigenvectors-eigenvalues
I'd suggest running it with BioVinci (https://vinci.bioturing.com) - no need to code to get all those stuffs.