Low Level Jet
Simply put, a low level jet is a narrow air current found in the lower atmosphere, typically at around 850 hPa (or around 1500m above the surface). Like the major polar and subtropical jets, they are "rivers" in the atmosphere, although on a smaller scale and generally at slower speeds. Similarly, they are the result of temperature gradients at lower altitudes, that lead to a pressure gradient and a flow of air perpendicular to that gradient, as a result of the Coriolis force. These jets can form in association with mid-latitude cyclones, mountain ranges (barrier jets), valley exits and sloping terrain. 
Mid latitude cyclones can contain several different types of low level jets, associated with both the warm front and cold front. The warm conveyor belt transports warm, moist air northwards within the warm sector. As it is transported northward, it ascends isentropically (in order to conserve potential temperature) into the storm: this conveyor belt provides the energy input into the developing cyclone. Likewise, a cold conveyor belt may develop ahead of the advancing warm front. This transports relatively cool air into the cyclone, where it too ascends isentropically. Both flows are ultimately forced westwards at high altitude, as they encounter the mid-latitude westerly winds aloft.
Ahead of an advancing cold front, winds often increase rapidly, generating squally conditions. This is associated with a wind maxima at around 850 hPa, assocaited with the differential pressure at constant height across the front. Behind the cold air, constant pressure surfaces decrease rapidly with height, meaning that at 1500 m, for example, the pressure will be lower than at 1500 m in the warm sector air, where constant pressure surfaces decrease less quickly with height. This means that pressure aloft in the warm air mass is greater than in the cold air mass, leading to a pressure gradient from the warm to the cold air. The flow is eventually turned to the north by the Coriolis force, generating a low-level jet. 
Conceptual model of a mid-latitude cyclone, indicating the rough positions of the conveyor belts. 
From: http://apollo.lsc.vsc.edu/classes/met130/notes/chapter12/warm_cold_conveyor.html
Barrier jets may form in the presence of a mountain range, and can persist for several days or more, given the right conditions. When cold, stable air approaches a mountain range, it is usually blocked and prevented from simply ascending over the mountains. This is often the case with strong cold fronts, which produce a large temperature inversion, with much colder air close to the surface. As the cold air sits below the tops of the mountains, a pressure gradient develops between the cold air and the warmer air at the same height further away from the mountains, with higher pressure associated with the cold air, and low pressure further away from the mountains. If the cold air pools below the mountains for more than a day, then Coriolis deflection will accelerate the flow perpendicular to the mountains, generating a barrier jet. 
Schematic of the formation of a barrier jet. 
Credit: COMET/ MetEd
A low level jet may also develop in response to a pressure gradient associated with sloping terrain. This is a prominant feature associated with the Great Plains of North America, which slope gently from east to west, towards the Rocky Mountains. The nocturnal low level jet can often lead to the initiation of long-lived mesoscale convcective complexes that produce heavy overnight rains in this region. The formation of this jet is still mysterious, and there are several theories that have been proposed, but none of which provide a conclusive argument for their formation. The theory I will discuss shows that the low level jet can form in the same way as a jet associated with a cold front. 
Diagram illustrating the direction of the low level jet during day and night. 
From: Mesoscale Meteorology in Midlatitudes textbook, by Markowski and Richardson. 
During the day over the sloping Great Plains, the surface heats up. This means that over the western Plains, the air is heated more than the air over the eastern Plains at the same height, as the surface slopes downwards. Therefore, the air is warmer at 850 hPa (for example), further west. This results in higher pressure in the warm air and lower pressure in the cooler air - as the pressure surfaces decrease with height more rapidly. The Coriolis force deflects the air movement to the right (south in this case), giving a northerly low level jet during the day.
At night, the situation is reversed. The surface cools more rapidly than the air above it, and so air to the west is cooled more than air further east at the same height. Low pressure associated with the cold air and higher pressure associated with the cool air to the east results in a flow of air from west to east, which is defelected to the north by the Coriolis force. Therefore, a southerly flowing low level jet will develop during the night, known as the nocturnal low-level jet.