The book of Psalms is the 19th book of the Bible, appointed for use in Christian worship. Translation from the original Hebrew text, produces a book in our English Bibles which does not conform to regular "verses" (or meter) necessary for ease of singing in. To address this the Metrical Psalms are a translation which preserve the meaning of the Hebrew original, while providing verses structured for singing in a regular meter to enable singing in praise to God.
All singing in public praise is A capella Psalm singing: that is singing of the psalms unaccompanied by musical instrument. Many recordings contain only melody, however some contain 4 part psalm singing: that is singing of Soprano (melody), with Alto, Tenor and Base harmonies.
Meter refers to the number of syllables on each line of a tune. Translations typically utilise a number of frequently used meters, although some psalms are sometimes set to a meter not used for any other psalm. In addition some translations translate a psalm to 2 or more meters (normally "common" meter, and another meter).
As most meters are used for more than one psalm, it is possible to sing different psalms (with a given meter) to the same tune. Clearly some tunes are more suitable to some psalms the others (e.g. a joyful tune to a joyful psalm).
Psalm Singing Online has been established to provide recordings of the metrical psalms, together with other materials of interest to Psalm Singers.