What is the upper 100 alpha percentile for chi-square distribution and why use it?

Question

Recently, I learned about the chi-square distribution.In my class I was told about the upper $100\alpha^{th}$ percentile $\chi^{2}_{\alpha}(k)$ and given the following definition: $$P(X<\chi^{2}_{\alpha}(k))=1-\alpha$$ $$P(X>\chi^{2}_{\alpha}(k))=\alpha$$ I have tried my best while looking online for additional information using a given name but got almost nothing( I do admit I might have looked for the wrong thing). Can someone tell me the formal name of this concept? Additionally, why would we even have something like this if a general concept of percentile should be sufficient? Also, do we use it anywhere else outside of the chi-square distribution?