In "We did have two days of rain" did adds emphasis to the sentence, i.e. we really had lots of rain for two days.
"We had some rain." That's just stating the fact that it rained for two days.
The structure subj+did/do/does+bare infinitive is meant to be emphatic: some emphasis is being added to what is being said.
I did tell you he was only trouble.
Hope it helps
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