Final answer:
NGC 6791 is an open star cluster that is considerably older than many other clusters, with an estimated age of 8 to 9 billion years.
Step-by-step explanation:
The stellar age of NGC 6791 is significant because it is one of the oldest known open star clusters. The age estimates for NGC 6791 vary, but most studies suggest that it is around 8 to 9 billion years old. This is much older than the clusters depicted in various provided figures, such as the relatively young NGC 3293 at approximately 10 million years old and NGC 2264, in the Christmas Tree Cluster, at about 2600 light-years away. NGC 6791's considerable age provides astronomers with a valuable opportunity to study long-term stellar evolution and the dynamics of star clusters as they can compare it with younger clusters like NGC 3293 and NGC 4755, the latter being an open cluster at about 6400 light-years away known as the Jewel Box for its variety of star colours.