All else being equal, net income produced by a company, attributable to its shareholders, is a fundamental driver of the value of a share. Many other things are relevant and should be considered (Is net income high because, like TSLA in 2020, you had a $1B+ speculative gain on trading BTC?), but net income is a simple comparison point to start analysis from.

Now, how does that net income relate to you personally, as an individual investor?

From an investor's perspective, the value of that net income is relative to your ownership. Earnings of $1B, when you own 1% [ie: $10M attributable net income, is in some ways the same as having 10% ownership of $100M]. So it's really NI-per share, that indicates what your share is actually worth, because different companies naturally have different numbers of shares outstanding. In theory, it might make it easier to compare an investment into Apple vs Microsoft - simply put, if Apple earns $100 per share every year, and Microsoft earns $50 per share every year, you might say, simplistically, that if their future outlook is the same in the eyes of the public, an Apple share should cost 2x a Microsoft share.

In short - EPS is touted quick shorthand that allows for rudimentary comparison of different companies. Be careful that you don't put too much weight into simplistic analysis, but in terms of what you could quickly make into an attention-grabbing headline, convention makes this an frequent choice.