"Moving the goalposts" is the concept of changing the claim (along with its requirements for a disproof) upon seeing one's claim about to be proven false.
The phrase of "moving the goalpost" may relate to an analogy of a racer about to reach the finish line, only to find that the goalposts marking the finish line have been moved as the racer comes close to crossing it.
The following is an example of "moving the goalposts" in a conversation between a theist and a skeptic.
Theist: I prayed to God to heal me when I was sick, then I got better, proving that God exists. Skeptic: But the human body has the ability to heal itself; how is your recovery from illness proof of God's existence? Theist: Who else but God would have made the human body with the ability to heal?
In this exchange, the theist is changing his claim of proof of God's existence from "God healed me when I was sick" to "God gave made me with the ability to heal myself" after hearing the disproof of his first claim by the skeptic. In doing this, the theist challenges the skeptic to disprove this new claim while acting as if it were the same as the first.