"The names 'Psalms' and 'Psalter' come from the Septuagint (the Greek translation of the OT), where they originally referred to stringed instruments (such as harp, lyre and lute), then to songs sung with their accompaniment. The traditional Hebrew title is tehillim (meaning 'praises'; see note on Ps 145 title), even though many of the psalms are tephillot (meaning 'prayers'). In fact, one of the first collections included in the book was titled 'the prayers of David son of Jesse' (72:20).
"The Psalter is a collection of collections and represents the final stage in a process that spanned centuries. It was put into its final form by postexilic temple personnel, who completed it probably in the third century B.C. As such, it served as the prayer book (book of prayer, praise and religious instruction) for the second (Zerubbabel's and Herod's) temple and for use in the synagogues. By the first century A.D. it was referred to as the 'Book of Psalms' (Lk 20:42; Ac 1:20). At that time also Psalms was used as a title for the entire section of the Hebrew OT canon known as the 'Writings' (see Lk 24:44)." (The NIV Study Bible notes, Introduction to Psalms)
