알았어 and 알겠어 are very close in meaning. 알았어 is in the past tense form, which can also indicate the "perfect" aspect, like "I('ve) got it" in English. It signifies that one has understood something completely and/or has taken note of it, reassuring the other person. For small things, 알았어 is usually more natural than 알겠어. e.g. A: 나 먼저 갈게 (I'm off now). B: 알았어 (Okay). => a casual acknowledgement. 겠 in 알겠어/알겠다 softens the meaning like the English modals "would", "might", or "could". It can mean that one begins to get the idea or that one is ready to accept the idea or situation, similar to "I see / It makes sense to me." in English. It suits a more complicated or grave subjects better than 알았어, although the two phrases are interchangeable in the great majority of situations. e.g. A: 죄송하지만 그렇게 해 드릴 수가 없네요 (Sorry, but I can't do that for you) B: 알겠어요 (I see.) => response to a more serious subject saying one understands or accepts it.