What did king David accomplish during his rule?

Answer 1

King David accomplished many things during his rule from 1010-970 BCE. Namely, he wrote the book of psalms that ended up in The Bible. He united the Northern and Southern kingdoms into Israel, and he drove the Philistines from Jerusalem.

Answer 2

1) King David authored/compiled the book of Psalms and gave it to us in its present form (Talmud, Bava Batra 14b). The Psalms (Tehillim), which we might call the soul of the Jewish people, express the yearning of King David and of the entire nation to be close to God. They are one of the foundations of our prayerbook to this day.
2) King David was the one who finally succeeded in subduing all of the surrounding nations (see 2 Samuel ch.8 and ch.10) plus the entire territory of Israel, something which no one else did previously or subsequently. He succeeded in all his endeavors (1 Samuel 16:18).
3) He secured from the prophet Nathan a promise from God that his (David's) son Solomon would build the Holy Temple (2 Samuel ch.7). The First Temple is actually considered the accomplishment of David himself (Rashi commentary, Berakhot 18a), since it existed in his merit (Sefer Torat Chaim, commenting on Talmud, Shabbat 30a).
4) He set the blueprints, with Divine inspiration, for the Holy Temple (1 Chronicles 28:19). Together with the prophet Samuel, he located the spot where the Temple would be built (Talmud, Zevachim 54b); and he dug the foundations for the Temple (Talmud, Sukkah 53a).
5) He amassed vast amounts of material and precious metals for the construction of the Temple (1 Chronicles ch.29).
6) Together with Samuel, he instituted the 24 groupings of families of Kohanim and Levites (Talmud, Taanit 27a).
7) He served God all the days of his life (1 Kings 11:38); and God was with him (1 Samuel 16:18).
8) He was without peer in clarifying and applying the halakhot (laws) of the Oral Tradition (Talmud, Sanhedrin 93b).
9) King David serves as the archetype of the effectiveness of repentance (Talmud, Avodah Zarah 4b).