Jaar is the most common Hebrew word for “forest.” It refers to forests generally (Isaiah 10:18). It also refers to specific forests, such as the “forest of Ephraim” (2 Samuel 18:6) and the “forest of Hereth” (1 Samuel 22:5). Both of these forests are connected to King David's story.
The word jaar also appears in the name of one of King Solomon's buildings called “the Palace of the Forest of Lebanon” (1 Kings 7:2). This building seems to have gotten its name because it used a lot of cedar wood in its construction.
Only one mention of “Jaar” seems to be a proper name. In Psalm 132:6, there is a reference to moving the ark of the covenant from Kiriath-jearim to Jerusalem. In this verse, the place is called "the field of Jaar" (or “the wood” in the King James Version). This might be a shortened poetic way of referring to Kiriath-jearim.