1st Party is made by the company that produces the console. Zelda is designed by Nintendo.
2nd Party is made by companies that have very close ties with the manufacturer of the console. Rogue Leader is made by Factor 5 which is closely aligned with Nintendo.
3rd Party is made by companies with no ties to the console company. They pay a license fee to release games for the console and usually produce multi-platform games like EA with the Madden series.