The brown pot incident basically demonstrated that Silas had not lost entirely all his capacity to feel affection of some sort even after the situation that we went through with William Dane.
When Silas moved to Raveloe, he had brought with him a brown clay pot that he used for nearly everything. The importance of the brown pot is that he had had it for over 15 years. It is one of the very few things that Silas can consider loyal to him. He personified the brown pot as if it were a friend, or a companion, of many years.
When he tripped and the brown pot broke, he tried to put the pieces together but, since it was not possible to use the pot again, he saved the pot in a special place in his house, as a decoration, (also as a museum piece) to remind him of his years with the brown pot together, and as a glimmer of affection for this object which had withstood so much with him.