Say one has a program that performs PCA. The program calculates the number of PCs necessary in order to cover a given share of total variation in the data, e.g. 95 %.
Say the number of PCs necessary in order to cover 95 % of the variance is 10 for the data used at time t=1.
At t=2 we re-run the program with data from t=2. For t=2 the number of PCs necessary in order to cover 95 % of the variance is 5.
Hence the number of necessary PCs in order to cover 95 % of the variance has dropped from 10 to 5 from t=1 to t=2.
Main question:
Can we make any conclusions about changes in the data from t=1 to t=2 in this case?
Example:
Can we say something like: "Since the number of PCs decreases from t=1 to t=2, there is more correlation in the data at t=1 than at t=2. With more correlation in the data, fewer PCs are needed to cover a given share of the varaince in the data."
Yes, If the original variables are strongly correlated, a reduced number of components can explain 80% to 90% of the variance, and the percentage of variance corresponds to the percentage of information from your data, that has been kept by the PCs. Furthermore, if you'd like to have more details about PCA, you can read this great comment: https://stats.stackexchange.com/questions/2691/making-sense-of-principal-component-analysis-eigenvectors-eigenvalues/140579#140579