Reef lines are lines that are used to reef a sail (usually the mainsail). There are several different systems for reefing sails, but they all need to be able to firmly affix the reef points to the boom, and provide suitable tension aft to act as an outhaul while the sail is reefed.
It is common for sailboats to have anywhere from one to three sets of reefing lines.
A typical reefing system has a line that is run from a point on the boom, through a cringle in the leech of the mainsail, and then back down to a block or sheave on the boom. This line can be run forward through the boom, or along the outside to a winch where the line can be suitably tightened.