I have heard that people say the greater earning means greater
intrinsic value of the company. Then, the stock price is largely based
on the intrinsic value. So increasing intrinsic value due to
increasing earning will lead to increasing stock price. Does this make
sense ?
Yes though it may be worth dissecting portions here. As a company generates earnings, it has various choices for what it can do with that money. It can distribute some to shareholders in the form of dividends or re-invest to generate more earnings. What you're discussing in the first part is those earnings that could be used to increase the perceived value of the company. However, there can be more than a few interpretations of how to compute a company's intrinsic value and this is how one can have opinions ranging from companies being overvalued to undervalued overall.
Of Mines, Forests, and Impatience would be an article giving examples that make things a bit more complex. Consider how would you evaluate a mine, a forest or a farm where each gives a different structure to the cash flow? This could be useful in running the numbers here.