Psalms is a tricky one to try to summarize. This will be a bit different than many of my previous attempts to capture what I believe to be a useful way to summarize the books of the Bible.
Psalms is a book of compilations. As a matter of fact, it is five books of compilations. The first two of these books (Psalms 1-41 and Psalms 42-72) are believed to be compiled before the Babylonian exile, but the remaining three books (Psalms 73-89, Psalms 90-106, and Psalms 107-150) are believed to have been compiled after the exile to Babylon. Note that I am not saying these Psalms were written after the exile, but this is when they were compiled into a collection.
The Psalms were created by multiple authors including, of course, David. Besides David were Asaph (who is mentioned in I Chronicles 25), Solomon, the sons of Korah, Ethan the Ezrahite, and one even has Moses as its author(Psalm 90). Many of the Psalms either had unknown authorship or the author is simply not recorded for us.
Each of the Psalms has a wide variety of formats, purposes, themes, and emotional emphasis. They range from straightforward exclamations of praise to God(Psalms 9 &35 for example), to lessons aimed at future generations(Psalms 14 &15), to honest cries of confusion and frustration(Psalm 10), to crys for help and protection(Psalm 6). There are many that have intimate connections with stories we can be familiar with from the historical narrative found elsewhere in scripture. Most of these can be found in either books one or two(Psalms 3, 7, 18, 30, 34, 51, 52, 54, 56, 57, 59, 60, & 63). However, there is one in Book 5 also(Psalm 142).
To me, the greatest trait that Psalms has is, perhaps more than any other book in the Bible, it makes it clear that those who are pursuing God with their whole heart can still express their most intensely personal thoughts openly to their God, and He will still love them and help them in their struggles. The spectrum that runs from the confessions of feelings of despair and being forsaken(Psalms 13 & 22) to those that express a confident assertion in their God(Psalms 16 & 18) reflect that God is not a tyrant who wishes to be appeased, but a parent who loves, and while wanting to be pleased, shows mercy and patience with his children as they come to recognize how amazing and trustworthy He is.