Probably the simplest part of a bike is the handlebars. No moving parts. Essentially just a tube. However they cause a large amount of confusion! There are so many "standards" and measurements. Here are some definitions (Thanks to Velo Orange).

• Flat Handlebar
• Handlebar that features no rise: Postino, Belleville, for example.

• Riser Handlebar
• Handlebar that features a rise for an added upright position: Left Bank, Montmartre, Porteur (can go either way up or down), Milan, and Tourist.

• Stem Clamp diameter - The measurement outside to outside of the area that clamps to the stem. 
• 26.0mm - standard road handlebars
• 25.4mm - standard city, upright, and MTB bars
• 31.8mm some more recent road and MTB bars particularly carbon fibre ones.
• Internal diameter - This is what you need to know if you are fitting inverse brake levers such as Dia Compe and Tektro. Generally a stem clamp diameter of 22.2mm corresponds to an internal diameter of approx 16mm and 23.8mm corresponds to approx 18mm. This can very slightly due to different manufacturers using slightly different gauges of tubing. If you have Steel bars, you will need to check as, as steel tubing usually has thinner walls.

• Brake Lever Clamp diameter - The measurement outside to outside of the bar where your brake levers and shifters clamp.
• 23.8mm - standard road components: think bar-end shifters, integrated brake/shift levers sometimes referred to as "brifters," road brake levers (aero and non-aero), interruptor or "cross" brake levers, and Guidonnet levers.
• 22.2mm - standard city and mountain components: trigger shifters, grip shifters, and some inverse brake levers.

• Width - Measurement from center to center of the ends of the handlebar.

• Rise/Drop - Measurement from center of stem clamp to the center of the start of the grip area. 

• Sweep - Measurement from center of stem clamp to bar end.

• Grip Length - Measurement of straight area of grip from end to end.