The answer is: He claimed that living for an extended period in areas where slavery was forbidden made him free.
Dred Scott was a slave in the southern states. At that time, he knew that northern states had prohibit the act of slavery, so he ran to those states hoping that he would obtain his freedom.
But his owner eventually know about his whereabouts and asked for government's assistance to bring him back. Scott sued his owner with the basis that since he had been living for an extended period in areas where slavery was forbidden, he should be regarded as free citizen.
He eventually loss in the supreme court and forced back into slavery.