tl;dr A European medieval sword, but with one edge instead of two.
The English ”falchion” is derived from the French ”Fauchon”, spelled as ”fawchon” in late 14th C texts. Behind these names lies the Latin ”Falxs,” describing weapons with scythe-like blades.
Falchion blades are typically rather short and broaden towards the point with the edge in a more or less sweeping curve. The hilt usually follows the popular styles as seen on double edged swords of the same period.
Two general shapes are predominant:
1. The first is curved more or less like a saber usually with a short clip point.
2. The second has a straight back with or without clip point, and a curving edge.