These are the sponsor’s requirements to pay you their specified bonus. If it says: “Finish: >=5”, this means that the sponsor wants you to finish in the Top 5. If a sponsor lists another company as a requirement this means that you have to beat the team that that company sponsors. (You can click the company name to see which team they sponsor. If there is no team listed they are not sponsoring anyone.)
You must meet ALL sponsor requirements to get the sponsor bonus. If a sponsor has "NA" as a requirement you need only to participate in the race to get the bonus. If a sponsor lists another sponsors to beat that has not signed a team, any requirements involving that listed sponsor are automatically attained.