* 이해하다 (ihaehada): This is the most common and general way to say "understand," implying comprehension of facts or ideas. It's a verb.
* 알다 (alda): This means "to know" or "to understand." It's more about knowing something as a fact, rather than necessarily grasping a complex idea. It's also a verb. You might use this for simpler understandings.
* 알겠습니다 (algesseumnida): This means "I understand" or "Okay, I got it," and is a polite and formal way to respond to someone's explanation or instruction. It's a declarative sentence.
* 이해했습니다 (ihaehaesseumnida): This is the polite and formal past tense of 이해하다 (ihaehada), meaning "I understood."
The best choice depends on the context. For most situations, 이해하다 (ihaehada) or 알다 (alda) are good choices, while 알겠습니다 (algesseumnida) is best for showing you've understood something someone has told you.