When the sun is out or there's blue sky, why does it thunder?

There can be "lightning" at any time in the atmosphere. You can usually see it well on a hot night with a clear sky, also known as "heat lightning."

Since lightning is just the snapping of static electricity, then a thunderclap can occur.

Or you just experienced the tail end of a jet going supersonic. But there's not telling for sure.

Heat lightning as David writes, is a good idea. But here is a better one; positive lightning. Usually, during a thunderstorm, the base of the clouds is charged negatively. By induction, the earth under is then charged positively. But the top of the cloud is also charged positively and in a rare occasion, a lightning bolt happens between the top of the cloud to a distant place on earth that is then relatively negative. When it happens, it is as "thunder from a blue sky" because that distant place is perhaps away from the cumulonimbus that forms the thunderstorm. Google positive lighning and perhaps you will see that it is what you described.

It may not be thunder. If you have an air base nearby, it could be sonic booms.