Technology plays an enormous role in history, by allowing historians to analyze data that used to be inaccessible. 

In the 1920s and 30s scientists tended to unwrap mummies to find out what the mummified body looked like.  Today we can use the technology of CT scans and other x-ray devices to look through the wrappings and find out who and what was mummified without removing the wrappings.  This has also allowed more detailed examination that couldn't be achieved in the past.  Such devices have also allowed exploration of areas that were previously unreachable, like the ruins of Herculaneum, and Ships that sank in water too deep for scuba diving. 

Many Historians piece together the past by analyzing documents.  However, many documents were written in different languages e.g. cuneiform, Egyptian heiroglyphs, Greek, Latin, or Hebrew.  This used to require weeks of painstaking work with translators fluent in these languages, and then re-analyzing the data, and re-translating for details lost in the translation.  Now, a computer can do the translation in just a matter of minutes, proofreading for inconsistencies and translating minor details that didn't come through takes only hours instead of weeks, and the picture that emerges is much clearer than it used to be. 

Finally, collaboration is much easier.  When historians wanted to collaborate they used to use letters (cheaper than telephone or telegraph for the length of conversation) which took weeks to deliver, and would frequently find same conclusions but wouldn't know it for weeks, and disagreement over credit for different discoveries arose.  Sometimes they could both be covering different angles on the same event, and be none the wiser about whether they should collaborate.  Today, e-mail, social networking, and cloud computing allow historians to check on each other's work, recognize opportunities for collaboration, and communicate new findings in just minutes with clear lines of credit. 

Technology does not play as large a role in the study of history as it does in some other fields, but it can be important.  This is particularly true when studying history that is farther in time from the present.  Since you have tagged this with “archaeology and Jamestown,” I will discuss Jamestown specifically in this answer.

While we do have some records about Jamestown, we do not have anything close to complete records about all aspects of the lives of the earliest settlers.  Technology can help us to fill in some of the gaps.  Perhaps the first example would be that technology can help us to actually find the physical site of Jamestown.  Things like ground-penetrating radar can be used to find evidence of historical settlements.  Technology can also help us to understand why the Jamestown colony had troubles early on.  Dendrochronology, for example, implies that there was a severe drought at the time that Jamestown was settled.  This does not show up in the records so only technology can tell us about it.  Finally, it was technology that helped ascertain that certain human remains at Jamestown had been cannibalized.  Technology also helped to tell us the likely general identity (a gentleman’s daughter rather than a servant) of the victim and that she had not been killed for the purpose of cannibalization.

There are many facts that we cannot get from historical records.  Technology can help us to uncover some of these facts.  Therefore, it is important in the study of history.

What role does technology play in archaeology and history?  

When we think of archaeology we may think of adventure, Indiana Jones, and hired help painstakingly brushing away dust and dirt from the precious relics of times past.  This is not the case for the modern archaeologist, though adventure is still part of the thrill.  Modern technology has allowed archaeologists to use advanced excavation techniques, enabling greater recovery of fragile artifacts.  Using technology that ranges from lidar to x-ray guns, archaeologists can view sites without disturbing the soil and the objects beneath.  This allows for greater care and planning so that archaeologists can evaluate the layout of the excavation site to allow for maximum preservation of the artifacts, skeletons, and structures.  It also allows for preventing unnecessary excavation, preserving the surrounding landscape of the site.  Using advanced techniques, we have been able to peer deeper into the past than ever before.  A perfect example of this would be the study of the condition of the teeth and bones of ancient people through the eyes of modern dentistry and medicine.  Using their remains, we gain an insight into the health, diet, lifestyle, and cause of death of the subject.  As medical science advances, every bone that is recovered tells a piece of their story.