I use that construction a lot. I mean that it happens less than "common" but more than "uncommon." So, if someone asked "Are there always early morning meetings?" If there were early morning meetings every day - I would say "Yes." If there were 3 meetings/week, I would say "It's pretty common." If the last time this happened was last year, I would say "Never." If it happens about 3 times a year, I would say "It's uncommon." But if we end up having about one or two meetings a month... that's too infrequently to be "common." But it happens too much to be "uncommon." So "It's not uncommon" with a stress on the "not" and the "un."

I agree with the two other responses. It's like saying "it's not exactly common, but it isn't a strange occurrence either".

Yes and no. From a logical point of view you are correct. However to say that something is common is rather direct and absolute. I do not know the context of that sentence, but please keep in mind that "common" has also a derogatory and judgemental meaning (for instance, 'She's as common as muck'). As a rule, you should always be very careful when you say that something or someone is common, because it could be interpreted as an insult. I would stick with Mr Tom Jones in saying, "It's not unusual". To learn more about why people prefer to say "it is not uncommon" instead of "it is common" (possibly more so in British English) please read the article on understatement on Wikipedia https://en.wikipedia.org/wiki/Understatement

Yes. We sometimes say it this way for a dramatic effect or to "soften" the commitment of our statement. For example, perhaps I don't want to admit that something is common. I may say, "Well, it's not uncommon."

@Colin thank you!