One of the main functions of a bearing is to provide a low friction casing and support for a rotating shaft or axle. When you think of bearings, you probably think of ball bearings, which reduce friction by rolling between the shaft and the casing. A journal bearing is a little more complicated, although is has fewer parts; 'journal' refers to the shaft, and the 'bearing' is just the lubricant.
In a journal bearing, the lubricant fills the space between the shaft and the casing. Once the shaft starts rotating at full speed hydrodynamic forces will cause the lubricant to spread evenly around the shaft, preventing it from touching the casing at any point. This results in very low friction. A journal bearing is only appropriate in situations in which the shaft will be moving at very high speeds, otherwise the lubricant will not form a self-sustaining hydrodynamic wedge (AKA a fluid bearing or oil wedge). Common usages include steam turbines, centrifugal compressors, and various pumps and motors.
When the shaft is just starting or stopping its spin, the speed will not be enough to for a hydrodynamic wedge to form; thus, these bearings are most often used in situations where the shaft will be rotating nearly all the time. Many journal shafts are coated with a substance called babbitt made from soft metals such as lead and tin alloys, designed not to gouge and deform when the shaft rubs against the casing.
Journal bearings have low friction and thus longer lifespans, and longer lifespans mean that the machines using journal bearings have less downtime in for repairs. The lubricant also provides damping against vibrations. That said, they are very tricky to construct properly, and even a well designed bearing can have problems. The temperature, shaft rotation speed, and lubricant exchange speed all have to be within certain limits, and these limits are different for different bearings, depending on the bearing length, viscosity of lubricant, and the different types of journal bearings available. You may have your bearing set up and purring along, only to have it suddenly develop an oil whirl or oil whip, in which the lubricating oil wedge becomes 'unbalanced', and wobbles or whips around the shaft.
The most stable (and, as it happens, the most expensive) type of journal bearing is a tilting pad bearing. The 'pads' are actually sections of the casing that can adjust their angles independently of each other to respond dynamically to variations in the hydrodynamic wedge. Other variations on the basic casing include oval rather than round cross sections, and ridges along the inside of the casing.
Journal bearings are the most common type of hydrodynamic bearing. Some thrust bearings are also hydrodynamic bearings.
These bearings usually use oil as a lubricant, but in some situations water is used, or even gas.
References:
http://www.reliabilitydirect.com/appnotes/jb.html
http://www.machinedesign.com/BDE/mechanical/bdemech6/bdemech6_18.html
http://www.bpb-co.com/products/history.php
http://en.wikipedia.org/wiki/Journal_bearing