It is important to know the different parts both for safety reasons and to be able to sail your boat as efficiently as possible. If you don’t know what to do when someone suddenly yells, “prepare to tack” or “watch the boom!” you may be in trouble.
Block: This is the nautical term for a pulley.
Boom: The horizontal support for the foot of the mainsail which extends aft of the mast. This is what you want to watch out for when changing directions in a sailboat. It can give you quite a wallop on the head if it hits you.
Bow: This is what the front of the boat is called.
Centerboard: This is a (usually fibreglass) plate that pivots from the bottom of the keel in some boats and is used to balance the boat when under sail.
Cleat: Cleats are what lines (or ropes) get fastened to when they need to be kept tight.
Halyard: Lines that raise or lower the sails. (Along with the sheets, aka running rigging.)
Hull: The hull is the body of the boat and consists of everything below the deck.
Jib: This is the sail at the bow of the boat. The jib helps propel the boat forward.
Genoa: A foresail which is larger in size than a jib.
Keel: The keel is what prevents a boat from sliding sideways ("making leeway") in whatever way the wind is blowing and stabilizes the boat.
Line: Lines are ropes. They are everywhere on boats. There is only one "rope" on a sailboat, the bolt rope which runs along the foot of the mainsail.
Mainsail: As the name implies, this is the main sail of the boat. It is the sail attached to the back of the mast.
Mast: The mast is a large, vertical pole that holds the sails up. Some boats have more than one mast.
Painter: This is a line positioned at the front of small boats. It is used to tie the boat to a dock or another boat.
Rudder: The rudder is how the boat is steered. It is moveable so that when you turn the wheel or tiller, the rudder directs the boat in the direction you would like the boat to go.
Sheets: The lines that control the sails. (aka running rigging.)
Spinnaker: The usually brightly colored sail used when sailing downwind or across the wind.
Stays and Shrouds: There are wires that make sure the mast stays upright, even in very heavy winds. (aka standing rigging.)
Stern: This is the term for the back of the boat.
Tiller: The tiller is a stick attached to the rudder and is used to control the rudder.
Transom: This is what we would call the butt of the boat. It is the back part of the boat that is perpendicular to its centerline.
Wheel: The wheel works the rudder, steering the boat.
Winch: Winches help bring in the lines. When lines are wrapped around a winch, a sailor can turn the winch with a handle, which will make it easier to bring in the lines.
2. Know about the different kinds of sailboats.
In general, if you are a beginning sailor you will most likely not be operating your own schooner. You will probably be working with a catboat, cutter, or sloop.
Sloop: Sloops are the most common type of sailboat (when you think of a sailboat this is probably the one you picture in your mind.) It has a single mast and is rigged up with a jib in the front and a mainsail attached to back of the mast. They can range in size and are ideal for sailing upwind.
Catboat: A Catboat has a mast set up near the front of the boat and is a single-sail boat. They are small (or large, for that matter) and easily operated by one or two people.
Cutter: Cutters have one mast with two sails in the front and a mainsail on the back of the mast. These boats are meant for small crews or groups of people and can be handled relatively easily.
Ketch: A Ketch has two masts, with the second mast called the mizzen mast. The mizzen is shorter than the main mast and is in front of the rudder.
Yawl: Yawls are similar to ketches with the difference being that their mizzen masts are located behind the rudder. The reason for this placement is that the mizzen on yawls is for keeping balance, rather than for moving the boat forward.
Schooner: Schooners are large sailboats with two or more masts. The mast in the back of the boat is either taller or equal in height to the mast at the front of the ship. Schooners have been used to commercially fish, transport goods and as warships.
3. Know common terms used on a sailboat.
Aside from the terms used for the different parts of the boat, there are also certain terms that sailors commonly use while at sea (or heading out to sea.) A trick to remember that port is left and starboard is right is that starboard has two ‘Rs’ in it, which is the beginning letter of ‘right’. Starboard, green and right have more letters than port, red and left. You can also keep in mind that "port wine is red". 
Port: When you are facing the bow (the front of the boat) the side to your left is the port side.
Starboard: Starboard is the right side of the boat when facing the bow.
Windward: As the name might imply, windward is the direction the from which the wind is blowing, upwind.
Leeward: This is also called ‘Lee’. This is the direction to which the wind is blowing, downwind.
Tacking: Tacking is when you turn the bow of the boat through the wind so that the wind switches from one side of the boat to the other. This is when you most need to be mindful of the boom, as the boom will swing from one side of the boat to the other when you tack (you don’t want to be in its way when it does that.)
Gybing (Jibing): This is the opposite of tacking, which means that it is when you turn the stern (or back) of the boat through the wind so that wind shifts to the other side of the boat. This is a more dangerous maneuver in a strong breeze than tacking since the boat's sails are always fully powered by the wind, and may react violently to the change in the orientation of the boat to the wind. Care must be exercised to control the boom during this maneuver as serious injury is a possibility if the boom travels across the cockpit uncontrolled.
Luffing: This is when the sails begin to flap and lose drive caused by steering the boat into wind or easing (loosening) sheets.
4. Understand navigational buoys.
It is important to look out for and honor navigational buoys--they'll let you know where the safe water exists. In Europe, on your way out of the marina, red buoys are almost always left to starboard while green buoys are left to port. (Remember, Red-Right-Returning). For North America this is the other way round.