When a market is created, the market creator can attach a resolution source address to it. There is a brief window in time (currently ~3 days) after the market is over during which that address (be it a contract or just someone's account) can report on the outcome. After that, there is a further window in time (currently ~3 days) where anyone can choose to dispute this report.
If the report is disputed, then the market will continue on to normal reporting as though the original report never happened. If the report is not disputed, it is considered the authoritative and final resolution of the market.
There are two bonds associated with this process. The first is a bond the market creator pays which they will get back if the final outcome of the market aligns with how the early report reported. If the early report does not align with the final outcome, then the bond is forfeited to reporters.
The second is a dispute bond that must be paid by anyone wishing to dispute the early report. The dispute bond holder will get back their bond (plus some bonus for taking the risk) if they correctly disputed (meaning the final outcome does not align with the early report). The dispute bond holder will forfeit their bond to reporters if the final outcome aligns with the early report.
The purpose of these bonds is to discourage frivolous/malicious behavior by making it so there is a financial risk associated with taking an action within the system. If you are confident the early report is wrong (e.g., it is cheating/lying), then the risk is low and it is well worth it to dispute the outcome. However, if you just want to be a dick and make resolution take longer, then you will need to place a bond that you know you'll eventually lose.