I am hoping to get an intuitive, accessible explanation of quantile regression.

Let's say I have a simple dataset of outcome $Y$, and predictors $X_1, X_2$.

If, for example, I run a quantile regression at .25,.5,.75, and get back $\beta_{0,.25},\beta_{1,.25}...\beta_{2,.75}$.

Are the $\beta$ values found by simply ordering the $y$ values, and performing a linear regression based on the examples which are at/near the given quantile?

Or do all of the samples contribute to the $\beta$ estimates, with descending weights as the distance from the quantile increases?

Or is it something totally different? I've yet to find an accessible explanation.