Can someone explain what で does in this sentence? I don't really understand it.
で (de) usually means "at" in English...kind of..
Think of "at" meaning the same as "because" like: "The answer to your problem is (AT) this cause." "We found what was (AT) the root of the problem." etc.
ato de = later. Not in a different place, but AT a different time or situation. (Unless you consider time a fourth directional dimension, but that's another forum!)
で can also mean "in". "in this situation" instead of "at this situation"
"in this case", or "in the case or", or "because of" special case-de, situation-de.
The same with "I'm at the pool", "I'm in the pool".. or movie theater, etc.