Caesar participated in, and was responsible for, a series of events that fundamentally changed the Roman world from a Republic into an Empire. Whilst Caesar was de-facto Emperor, or dictator, his adopted son Octavian became Augustus, the first Roman emperor. Future emperors would take the prenomen 'Caesar' and 'Augustus' in their names.
When Caesar was alive and kicking, the Roman Republic detested the idea of a single ruler, or King. To enter the boundaries of Rome itself with an army was treasonous. Caesar gained military acclaim and financial status after his conquest of Gaul. The ensuing fallout resulted in a civil war that ultimately ended with Caesar beating his rivals and becoming dictator/emperor. However, he was 'betrayed (however you want to view it)' by the people who he helped into power. He was assassinated in the Theatre of Pompey, prolonging the war and allowing his adoptive son to effectively 'claim the purple' after the battle of Actium in 31BCE.

Most of what we know about Roman history comes from ancient sources. It is very important to consider the context in which these sources are written, and how the authors feel about concepts of dictatorship, the past, the founding of Rome etc. Generally ancient authors were patronised by emperors, so they had to be careful of what they said. Considering that most emperor's were considered Augustus (lit. deified) and called Caesar, the lineage remains unsullied.

Secondly, the Romans (and Greeks) absolutely love a 'foundation myth/story'. Most ancient authors are writing well beyond the time they cover. The assassination of Caesar is just another chapter in the Annales of Rome.

Consider modern day empires. Napoleon's emblem was the eagle, as was Nazi Germany. The Weimar rules of Germany were called 'Kaisers' - a derivative from Caesar. Popular culture loves the story of Caesar. Shakespeare wrote about it. The list is endless (Starship Troopers, Warhammer, Rome-focused video games)

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TL;DR: Caesar was first Roman 'emperor'. Did a lot of important stuff in changing Rome from Republic -> Empire. Future emperors take his name. His role in political and social events were recorded by ancient authors in a generally positive light. Future media loves the story and tells it in many different ways.