"The Roman Empire", as most people understand it, meaning ancient Rome, is a period of somewhere between 500 and 1500 years spanning territory from Western Europe to Syria and from Northern England to North Africa.
The reason this is a meme is that it's the equivalent of asking "how often do you think about the US" and then being surprised that the answer is some number. If you have even a passing interest in things that happened not specifically right now the answer to this is nonzero.
Now, the weird part is how many of the memers are getting things completely wrong or just generally fantasizing about the... I don't know, look and feel of the thing. If and when I think back to this it's mostly about petty neighbourly disputes leading to lawsuits and crummy politics.