Lane’s parents arrange for her to attend a local hayride with a Korean-American teenage boy as her date. A hayride is a North American traditional activity where (as the name suggests) people travel in a wagon filled with hay for fun. They are a form of celebrating the harvest season, and may involve other activities associated with the fall.
Rory does not attend the teen hayride, not seeing anything about it she would enjoy (from what we see, the hayride does look pretty lame and boring, as it just goes around the main square in town, rather than through fields). However, in later episodes we learn that Taylor will not allow Rory to skip any town entertainments or functions, not even accepting illness as an excuse.
At this point, Taylor wasn’t a character in the show, although his name is mentioned later in this episode. It is possible that originally Rory was intended to be considerably more detached from the events of the town than she ended up being.
Rory missing the hayride does point to a disdain for teenage activities that seems in keeping with her character – perhaps because they would have meant having a life separate from her mother. This might be why Rory never seems to be popular with her peers, although adored by adults.