Monomolecular blades are forged from a super-hardened and dense material made of strongly-bonded carbon molecules, with the edges honed to the width of single molecule (specifically a buckytube molecule). Since blades cut better when their edges are thinner, blades one molecule thick would theoretically allow them to slice into things at the molecular level. In other words, it's an impossibly sharp blade that can cut almost anything.
Monomolecular blades can cut into almost anything, but not necessarily through. Given a thick enough object, friction will eventually slow the blade to a standstill. How deeply a monomolecular blade can cut depends on how much force is put behind the blow. Therefore, although a regular unawakened human could chop a cinderblock in half with one swing of a monomolecular blade, only someone supernaturally strong like a werecreature, vampire, ghoul, or mage could do the same to a boulder.
Monomolecular blades have a hard time cutting things made from the same or similar materials - specifically diamond, fullerene mesh, buckytube monowire, and other monomolecular blades. As fullerene mesh is one of the main components in armor plating, monomolecular blades are of limited use against troopers in power armor or armored vehicles like hovertanks. Although a forceful enough swing or stab might be able to pierce through or slice into a armored target, don't expect to be chopping a hovertank in half anytime soon. However, against unarmored opponents (including Arachnids), monomolecular blades are devastating.
Hacking at an armored target with a monomolecular weapon can eventually damage the blade. High quality monomolecular blades are tempered so as to resharpen themselves via flaking (i.e. a blow to the edge causes the material to flake, exposing a fresh cutting surface underneath). Poor quality monomolecular blades will become chipped, dulled, and blunted over time, and need to be periodically resharpened by a professional with specialized equipment.
Finally, monomolecular blades can be a danger to the wielder: one wrong twist or flip of the wrist could result in severed fingers or worse, and the cut would be so clean the person may not even notice it at first. Even if wearing protective gauntlets and armor, users should still be extremely careful when handling such potentially hazardous weapons.
Cost & Availability
Monomolecular blades will always be more expensive that an equivalent blade made of steel. Monomolecular knives and daggers are common, widely available and (although expensive) are still relatively affordable. Monomolecular swords are more rare and very expensive, but can still be found as many werecreatures in the old Tech Infantry preferred them as backup weapons for hand-to-hand combat. More exotic monomolecular blades (axes, spears, shuriken, etc.) are extremely rare, if available at all, and may have to be custom-made... and either way will be hideously expensive.
Monomolecular blades always come with special sheaths that store the blade in such a way that it won't simply slice through the scabbard and fall to the ground.
Behind the Scenes
A major inspiration to the treatment of monomolecular blades in TI comes from the magically-conjured sword with a "Black Diamond blade, with a monomolecular edge" from Her Majesty's Wizard by Christopher Stasheff.