Why is a functional dependency described as a "one-to-many" relationship? As far as I know, the definition of a functional dependency reads that, given the attributes X and Y, "each X value is associated with precisely one Y value". But then the author of the article that I read called this a "one-to-many" relationship. Isn't this really "one-to-one"..?
I think that the FD can't be described as "One-to-one" relationships. In One-to-one relationships, the X value identifies a Y value and vice-versa. In FD this doesn't happen. In fact, the Y values can be shared from different tuples with the same X value.

Think to a simple table with only cities, states and nations (And don't care about the redundancy). We know that the state identifies one and one nation, but a single nations doesn't identify a single state.

So, generally  X implies Y but Y doesn't imply X.

A last observation: an one-to-one relationship need that the tables involved in the relationship must have the same number of rows, in order to associate to every a one b and to associate to every b one a. In the textbook you'll find a lot of FD in which this doesn't happen.

So we can describe a FD as an association of a Y value to many (only sometimes one) X values. So it's called an one-to-many relationship.