The chapter
Simply An argument about washing hands before eating turns into a question about where uncleanness actually comes from. His answer is that nothing going into a person from outside can make them unclean, and that what does comes out of them.
Context Mark stops the story to explain the custom, that the Pharisees and all the Jews wash before eating according to the tradition of the elders, and that there are washings of cups and pitchers and bronze vessels besides. It is the kind of aside a writer adds for readers who do not already know, and it is one reason his gospel is thought to be addressed to people outside Judea. The disagreement it introduces is between him and one group over one practice, argued from Moses and Isaiah on both sides of it.
Verses 1-13
Simply Pharisees and scribes who had come from Jerusalem ask why his disciples eat with unwashed hands. He answers with a line from Isaiah about a people who honor God with their lips while their heart is far from him.
Context The example he picks is money owed to parents. A man could declare that what his father or mother might have had from him was Corban, given to God, and after that he was no longer allowed to use it for them. Against that he sets the commandment to honor father and mother, and calls the result a tradition that makes the word of God void.
Verses 14-23
Simply Then he calls the whole crowd and says it in one sentence, and the disciples still do not follow it. They ask him about it afterward, in a house, away from everyone.
Context His explanation moves the whole question from the stomach to the heart: what enters does not reach the heart, and what comes out of the heart is what defiles. As the World English Bible renders the end of that clause, it also makes all foods clean. The list that follows is long and almost entirely about what people do to each other: evil thoughts, murders, thefts, deceit, envy, pride, foolishness.
Verses 24-30
Simply In foreign territory he goes into a house wanting nobody to know, and cannot stay hidden. A woman, a Greek and a Syrophoenician by race, falls at his feet and asks him to free her daughter.
Context His first answer is no, in an image about letting the children eat first rather than throwing their bread to the dogs. She takes the same image and turns it: even the dogs under the table eat the children's crumbs. He grants it on the strength of what she said, and Mark says so in as many words, that for this saying the demon has gone out of her daughter.
Verses 31-37
Simply A man who is deaf and can barely speak is taken aside, away from the crowd, and healed with fingers, spit and a sigh. Mark keeps the word as it was spoken, Ephphatha, and translates it for the reader: be opened.
Context He tells them to say nothing, and the more he tells them the more they spread it. What the crowd says at the end, that he makes the deaf hear and the mute speak, is close to the words Isaiah uses for the day the deaf are unstopped and the tongue of the mute sings.