The answer to this can be found in Chapter 10, the longest chapter in the book. There, we see that Douglass has written passes for himself and some other slaves. They were going to use the passes as a way of escaping. The slaves needed the passes to show that they had their master’s permission to be out and about. Douglass destroyed the passes because he knew that he would be in serious trouble if they were found.
The escape plan that Douglass and his fellow slaves had concocted had been betrayed. They were going to be interrogated about the alleged plot. If the passes had been found, it would have been clear that the allegations were true. It was also likely that Douglass would have been in particular trouble for forging the notes. Luckily for Douglass, one of his fellow slaves caused a commotion by struggling over being tied up. During that time, Douglass was able to throw the passes in the fire. As it turned out, the slaves who had been planning to escape essentially got away with it because the evidence had been destroyed.
We can see that this is the case from the following passage:
Mr. Hamilton suggested the propriety of making a search for the protections which he had understood Frederick had written for himself and the rest. But, just at the moment he was about carrying his proposal into effect, his aid was needed in helping to tie Henry; and the excitement attending the scuffle caused them either to forget, or to deem it unsafe, under the circumstances, to search. So we were not yet convicted of the intention to run away.