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What do the blue factions points do?
I believe you mean the blue number next to the sale price. That is the amount of guild exp you get per item. Faction is awarded (or subtracted) for killing rival mobs or completing rival quests.
Guild exp and your personal status are different. Guild exp will just raise your guild level and eventually unlock items at the city merchants.
When you complete a quest and get faction, it will raise your favorability with them, eventually unlocking titles for purchase.
Personal status can be used to reduce the cost it things such as a horse. So insted of paying 2pp for a horse, you can pay 1p10g + 30,000 status.
I believe at guild level 30 you can purchase a Spirit Horse or Flying Carpet for 60pp and 1 million status.