Paying respect to a faction can be done periodically. Doing so earns you a single Stat Point and a number of Affiliation Points for the faction you pay respect to. Reaching certain levels of affiliation points for a faction grants you certain rewards.
For most factions, paying respect grants you 100 affiliation points and you can pay respect again 24 hours later.
For the Cartel, paying respect grants 200 affiliation points and you can pay respect again 48 hours later (this reflects the fact that the Stamina point granted would cost two skill points whereas every other stat point costs just one).
There are Achievements that can be earned by paying respect.