The most romantic word in mathematics.
Imagine two arcs so slightly pushed up against each other so that there is only a single point at which they intersect. That is osculation.
The image is too cute to resist though, so it has picked up the secondary meaning of a kiss. I found the term in the noir potboiler Dark Blond by David Fears. Keeping with the geometric definition, I imagine the quickest of pecks or the chastest of kisses.
UPDATE: So much complication. First, I was shocked by how many math people have never heard of this word. Secondly, it seems like it could mean two separate things. While it could mean to curves that touch at a single point, it could also mean two curves that run alongside each other without ever crossing. Like this:
This would suggest a very different meaning than the slight peck on the cheek, hence, a google search of the term also comes up with: