The word "psalm" is derived from a Greek word meaning "song." But before these poems were translated into Greek, they were written in Hebrew. In Hebrew the Book of Psalms is called "Tehillim," which means "praise song." A psalm was written as a song, perhaps accompanied with a lyre or harp. You'll often notice that traditional images of David, the supposed author of Psalm 23, show him with a harp in his hand. That's because he is known as the singer of the psalms.
The psalms are sometimes called "Hymns of Praise." Modern famous modern poets, like Gerard Manley Hopkins, have drawn inspiration from the psalms to write their own hymns of praise (check out his "Pied Beauty" and "God's Grandeur"). Not all of the psalms are devoted to praise, but many of them are. Some scholars believe that the word "praise" indicates that the psalms were intended for use in formal religious services, which were largely dedicated to the praise of God (source).
The psalm had no title except for "Psalm 23," but many people refer to it using its first phrase, "The Lord is My Shepherd." We have no idea whether the original author, whoever he or she may have been, used a formal title or not.