I'm not sure what you're referring to. Ignoring the question of historicity of the Biblical account, the typical tale is that King David was the one who conquered Jerusalem itself, and declared it to be the capital himself as well. This was continued by Solomon. Both ruled, according to the Biblical story, a united kingdom that combined both Judah and Israel, and King David came from Judah to essentially conquer Israel and unify it into one kingdom.

Each has Biblical tales associated with them that make them as famous as they are. For example, lawyers today use the term "splitting the baby" to refer to cases where a judge might choose to give both sides part of what they want, which is a reference to the story of Solomon threatening to split a child that two women were arguing over (to figure out who the real mother was, by seeing which was willing to give up just to avoid harm to the baby). You can read the story here. King David is also described Biblically as the source for the ancestral line that will eventually result in the coming of the Messiah, in Jewish tradition (see Isaiah 11:1, which says the Messiah will come from the "line of Jesse", Jesse being the father of David). The Biblical focus on these two likely plays a large part in their prominence, as does their ability to unify and keep unified the two kingdoms under one united kingdom. They did also control a decent swath of land, likely around 40 miles from end to end in the Judah portion alone (from Jerusalem to Beer Sheva, if not more than 40 miles), which is certainly notable, even if it pales in comparison with empires like the Roman Empire. David's decision to move the capital to Jerusalem following its conquest is not really explained in the portion describing its capture, but it likely rests on the description later of David's being commanded by God in the Biblical tale to buy and build an altar there, which later became the Temple under Solomon and is known today as the Temple Mount. We can only speculate as to when and how this all really took place when we discuss the historicity problem, but since your question is about fame, Biblical importance is a key aspect. David was commanded to build the altar, and Solomon built the Temple, on the spot where Abraham was set to sacrifice Isaac in the ultimate test of faith, in the Old Testament tradition. This likewise added to its importance as a city, and to its holiness. 2 Chronicles 3:1 says:

Then Solomon began to build the house of the LORD at Jerusalem in mount Moriah, where [the LORD] appeared unto David his father; for which provision had been made in the Place of David, in the threshingfloor of Ornan the Jebusite.

And similarly, one can look back to Genesis 22:2, which says:

And He said: 'Take now thy son, thine only son, whom thou lovest, even Isaac, and get thee into the land of Moriah; and offer him there for a burnt-offering upon one of the mountains which I will tell thee of.'

And thereby you have a sort of continuation of the location, and the importance of it in the Jewish (and later Christian and Islamic, though the Temple Mount holds additional significance to both for other events) tradition. So David and Solomon were essentially more prominent because they ruled a united kingdom of Israel, and were not only commanded directly by God in various ways to do things (at least, David was), they also expanded on the holiness of Jerusalem that had been held previously by the Jebusites, according to the Biblical tales at least.