Okay, I have little to no knowledge on this whatsoever, and I have no idea what to look up or else I would have found this out myself. Basically I hear a lot about there being an emperor, and under an emperor a caesar and that there were 2 emperors and 4 caesars? Could someone please correct me and explain what this is? Thank you.
The idea of the tetrachy was that the Roman Empire was too big and was surrounded by too many enemies on all sides to be dealt with by one man alone. So the obvious answer is to get two rulers, one to take care of the east and one to take care of the west. This is what Diocletion did in 285 when he made his comrade in arm Maximian his Caesar, he was elevated to the rank of Augustus in 286. This was known as the Diarchy, the rule of two. But what happens if one Augustus falls in battle or dies? There needs to be someone to take over so that the frontiers are not overrun. So the imperial college was again expanded in 292 to include Constantius Chlorus and Galerius who were made Caesari, junior emperors. Diocletions then attempted to create a mechanism to secure the succession, something that the Roman's had had a huge problem with for years. The Augusti would abdicate, as he and Maximian did in 305, and allow the Caesari to ascend to the rank of Augustus. New Caesari would then be appointed and the cycle would start all over again. I believe the idea was that that Caesars would cut their teeth on the border regions and would then ascend to the rank of Augustus as an experienced commander and administrator.
Things began to get messy later on for a couple of reasons.
Firstly, the tetrachy only worked when there was one emperor who was indisputably the most important Emperor. In the initial stages this man was Diocletion. He was the man who appointed the Caesari and he was able to force the abdication of Maximian (he never really wanted to retire anyway) who quite quickly declared himself emperor again in 306. Once there was no authority to stop them the emperors began to fight amongst each other and declaring themselves emperors and coming out of retirement. Shenanigans like that.
Secondly the entire system did not take account of the fact that the emperors had ambitious sons. This led to the sons of emperors declaring themselves emperor when there was already an Augustus and a Caesar. Examples include Constantine himself, after the death of his father Constantius Chlorus, and Maxentius son of Maximian then the entire system began to fall apart.
Civil war then ensued pitting Constantine against Maxentius, Licinius against Maximinus Daia and finally Constantine against Licinius until eventually Constantine came out as the sole ruler of the Roman Empire again. He then started again, dividing the empire amongst his three sons (made Augusti) and various nephews (made Caesari), causing another set of civil wars.
We should note that the tradition of naming Caesari, junior rulers or whatever, persistend long after the Tetrachy vanished, with Byzantine emperors often making their heir presumptive Caesar. If I haven't answered as you would like I will try to explain further.