Leaf mold is pretty much what it sounds like: leaves that have decomposed through fungal growth.1 It is the next step in leaf decomposition after leaf litter, and is midway to humus.
Leaves2 take a long time to decompose; while many gardeners will find ways to compost leaves more quickly, in the woods leaves take at least two to three years to break down to soil. Leaf mold will be identifiable as the remains of leaves, but will show significant degradation. Technically this is the F layer of the O Horizon (or, if you prefer, the O1 horizon); the plant matter is largely decomposed and some of the original structures are becoming difficult to recognize. This process will involve any number of decomposers; earthworms, bacteria, snails and slugs, small mammals, and others. However, the major player in this process will be filamentous fungi3, as the fungi are the most effective producers of the enzyme that breaks down the tough lignin in the leaves.
Leaf mold is usually dark brown to black, is crumbly but may be somewhat cohesive (due to the aforementioned filamentous fungi), and has an earthy aroma that is usually described as pleasant. In most forests the layer of leaf mold is rather thin and full of roots, so it is generally not harvested from its natural habitat. However, gardeners may use a separate compost pile just for leaves so that they can 'grow' leaf mold. This generally involves shredding leaves and leaving them to rot for about a year, watering occasionally to make sure that the pile remains damp. You can get just as good leaf mold without shredding (and, in most environments, without watering), but it may take 2-3 years to get the decomposition you want. When leaf mold is added to the soil it increases the water retention and encourages earthworms and beneficial bacteria, but it does not have much nutritive value. When talking about gardening, usually there is no strong distinction made between leaf mold and leaf litter; if someone says they are using leaf mold as mulch, they are probably actually referring to leaf litter.
Warning: These footnotes are unusually pedantic. Do not read if prone to boredom.
1. Well, I lie. Mold, in this case, refers to loose earth, and the name doesn't actually have anything to do with fungi. (The two senses of mold may have shared a root ~900 years ago. Or maybe not.) But as it happens, fungus is a major component of healthy leaf mold.
2. Leaf mold is most often used when referring to leaf litter in deciduous forests or compost from deciduous trees; however, the same terminology is used for coniferous forests/trees. Grasses and forbs have much less lignin, and are generally not considered to form leaf mold.
3. In most cases the most effective decomposers of leaf litter are assorted members of the Basidiomycota, although various members of the Ascomycota also help. This sounds very specific, but together these phyla comprise the entire subkingdom Dikarya, AKA the higher fungi. In other words, Dikarya includes all fungi big enough to see, including all mushrooms, along with a good sampling that you will need a microscope to locate.