To get the feel of the syncopation of a hornpipe try this example. Take a simple melody like Harvest Home which is usually written as straight eighth notes. The first and third notes of every bar are played as if dotted and every other note is therefore shortened. This means that every second and forth note is connected to the note it follows, hence that bumpy feel.

My daughter is a step dancer and this really all comes together when you see how a hornpipe is danced.