Weather is a popular subject in folklore. Historically this comes from the very real need for farmers and sailors to be able to predict the waether to come. The folklore is based in observations not science, though sometimes science does confirm some of those observations.
Ash before oak the summer is all a soak, oak before ash the summer is but a splash.
Translation: This refers to the spring budding season. If an ash tree shows buds before the oak shows budding, then the summer will be a wet season. If the oak buds before the ash tree, then the summer will be drier.
Science tells us that the timings of the first buds to break are actually dependent on the spring temperatures. Generally oak buds first, so the proverb is not very accurate in predicting summer rainfall.