Refer to my article on wOBA from Sabermetrics 101 for more in-depth explanation.
Linear weights are run estimators which linearly estimate the relative weight of different events. In the case of wOBA, walks, hit by pitches, singles, doubles, triples, home runs, and implicitly outs have their values measured. In the case of FIP, strikeouts, home runs, walks, and (implicitly) balls in play have their values measured. Linear weights are generally context inaware, meaning they don’t take into account the context of an outcome. However, you can absolutely calculate linear weights based on base-out state (as I did years ago, or as TangoTiger describes in this article). Linear weights are calculated by finding the average change in run expectancy that happens when a certain event occurs.