(Ame futte ji katamaru; “The rain falls, and the earth hardens”)
Before the rain, soil may be loose and crumbly. When the rain falls, it turns the ground soft and muddy. But after the rain has ended and the earth dried, it is harder – and stronger – than it was before. Similarly, when bad things happen, stress builds and it’s generally unpleasant. But the same experience also leaves us more experienced and better prepared to face future stresses.
At this point we might nod and remember that what does not kill Nietzsche makes him stronger. But I get the impression that the expression is commonly used for relationships, specifically, recovery from fights. When two people fight, issues that had been bothering one or both members, but which went unmentioned for fear of unpleasantness, can be aired. If the fight is conducted properly, it allow those issues to be acknowledged and set the stage for them to be dealt with. A good fight, like most other well-done social activities, involves communication – and communication generally strengthens relationships.
雨 (ame) is the noun “rain,” and it’s followed (without any particles, in a mild deviation from standard / grammatical Japanese) by the te-form (conjunctive or continuative form) of the intransitive verb 降る (furu), “to fall.” The pattern repeats: 地 (ji, in this case, although it can also be pronounced chi) – “earth,” “ground” – for the noun, and the intransitive verb 固まる (katamaru), “to harden,” “to solidify.”
One of my sources notes that this kotowaza is only applicable when the trouble is resolved internally, rather than through the intervention of a third party. You can tamp down loose earth to make it firmer, but that’s not the same as it firming on its own after a rainfall.
(“Un, kanojo to no momegoto mo atta kedo, otagai ni iken ga wakatta kara, ima wa daijoubu da yo.” “Yokatta ne. Ame futte ji katamaru to iu shi ne.”)
[“Yeah, she and I had a fight, but now we understand each other’s point of view, so that’s alright.” “That’s good! Like they say, ‘From adversity comes strength.’ ”]