Homer's account of the Trojan War does in fact appear to draw its inspiration from actual historical events, specifically a series of conflicts between a Greece-based people group known as the Ahhiyawa (identified as the Achaeans) and a city called Wilusa (hellenized to Ilion, and identified with the ruins at Hisarlik, which has been identified as Troy.

There are ancient Hittite texts that refer to something called the "Wilusa episode", where a group called the Ahhiyawa were involved in hostilities against the city of Wilusa, sometime in the 1300s-1200s BC. Everything we know about the Ahhiyawa from these texts and other texts indicates that they come from the general area of Mycenae, in Greece. Most scholars agree that it is reasonable to identify the Ahhiyawa with the Achaeans, based not only on the linguistic evidence (very clear relationship between the Hittite word Ahhiyawa with the Anglicized Greek word Achaean), but also the geographic area that they are from.

Similarly, the connection between Wilusa and Troy is similarly strong. There is a clear linguistic connection between the two place-names. The Greek name for Troy is "Ilion", which is a loan word/cognate word to the Hittite name "Wilusa". Archaeologically, pretty much everyone agrees that the mound of Hisarlik is the ruins of ancient Troy, and this is borne out by not only its geographic location (which matches with everything we know about both Wilusa and Troy), but also the presence of certain features such as a water tunnel which are mentioned in Hittite texts, and also found archaeologically. So all the lines of evidence that we can bring to bear on the question agree that Troy = Wilusa = Hisarlik and it existed and was in a conflict at one time with a Greek people group known as the Ahhiyawa = Achaeans.

That's about the extent of what we can say about the historicity of the Iliad though. Some characters may be based on actual historical figures, for example we have historical mentions of a king of Wilusa named Alaksandu from around this time period (Alexandros was the birth name of the Trojan prince Paris).

However, Homer's account is likely very much romanticized and fictionalized. We have no evidence that any of the details of the story actually happened, and beyond mentions of Aleksandu, and possibly Pariyamaradu and Piyama-Kurunta (historical figures involved in conflicts with the Ahhiyawa, perhaps an inspiration for the character Priam), we have no evidence that any of the characters in Homer's epic actually existed.

Homer's Iliad is most likely a fictionalized retelling, a fun reimagining of an actual conflict, much like Inglourious Basterds is a fictionalized retelling of World War II (some characters actually existed, like Adolf Hitler, there was a real conflict between the countries that actually happened, but the event details and the characters have no basis in reality).

All we know is that yes, there was a war, and yes, the Achaeans attacked Troy, and beyond that, it's all Homer.

For further reading on this subject, check out:

Sagona, A G, and Paul E. Zimansky. Ancient Turkey. London: Routledge, 2009

Easton, D.F.; Hawkins, J.D.; Sherratt, A.G.; Sherratt, E.S. (2002). "Troy in Recent Perspective". Anatolian Studies (52): 75–109

Allen, Susan (July 1995). "'Finding the Walls of Troy': Frank Calvert, Excavator". American Journal of Archaeology 99 (3): 379–407

Wood, Michael (1985). In Search of the Trojan War. BBC Books; First Thus edition

The Trojan War, A. Salimbeti http://www.salimbeti.com/micenei/war.htm