There are two important aspects to this quote. First, there is the idea that a marriage is a long, ongoing process in which two people deal with one another. Second, there is the idea that the process will not always be easy.
Marriage is a process in which the two partners have to deal with each other as they find out more about one another and as each partner changes. It is not a thing that stays the same. We have to constantly readjust to one another as changes happen in our lives. We get new jobs, we move from place to place, we have children, we develop new interests. In all of these ways, change occurs and the partners have to constantly adjust. In this way, it is like a conversation.
The second part is perhaps more obvious. It is saying that all marriages will have problems at times. They may not come in the form of screaming fights, but they will occur no matter what. The implication of the quote is that dealing with these disputes is part of the "long conversation" that goes on between the spouses in a marriage.