It's kind of a strange name and no other kingdom that I know of called itself Two-something. Why not Kingdom of Naples and Sicily? Or just Kingdom of Sicily? Did people really called or thought of Naples as "Sicily?"
In 1303 the them Kingdom of Sicily (which controlled the south of Italy and the island of Sicily) lost the island of Sicily to the King it Aragon.
However, despite no longer ruling the island of Sicily, the rulers of what had been the Kingdom of Sicily (referred to as the Kingdom of Naples after Sicily was lost) continued to refer to themselves as the king of Sicily.
At the same time, the rulers of Aragon (who actually controlled Sicily) also referred to themselves (along side other titles) as the king of Sicily - resulting in two rulers who both claimed to be the king of Sicily.
When the Kingdom of Naples and Sicily were officially reunited in 1816, the term Kingdom of Two (i.e. both, not just one) Sicilies was used to reflect that there was now just the one crown, and not two separate crowns held by one person simultaneously.