I'm currently learning about chi square test and the way to see if my observed data fits the expected data is by looking up the chi square critical value table.
My question is, where do these numbers in the table came from?
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You can start with What is the meaning of p values and t values in statistical tests? thread to review the basic concepts related to hypothesis-testing. You can recall that $p$-value is "the probability of observing a test statistic at least as large as the one calculated assuming the null hypothesis is true".
Tables of critical like this one come from $\chi^2$ distribution (or other distributions depending on particular test you are using) and basically they are quantiles, i.e. "values at which the probability of the random variable is less than or equal to the given probability". They are chosen in such way to correspond to the "critical" $p$-values like 0.05, 0.01 etc. So basically, if test statistic is not greater then critical value, then $p$-value is not smaller then the one specified in the table.
