• 理解りかい — understanding
• 解決かいけつ — resolution, solution
• 解釈かいしゃく — interpretation
• 解散かいさん — dissolution (e.g. parliament, group)
• 解とく — to solve, to untie

解 is a 形声文字 (semantic-phonetic compound). The radical 角 (horn) and 刀 (sword) symbolize taking apart or untying something — originally a horn. The meaning extended to “undo,” “untie,” and by extension “solve” or “explain.”

この問題もんだいを 解といてください。
Please solve this problem.

その言葉ことばの 意味いみが 理解りかいできました。
I understood the meaning of the word.

The on-yomi カイ is common in compound words like 理解 and 解決. The kun-yomi とく is used when 解 appears alone or in simpler phrases.