The Mishna on page 18 states that to eat “chullin” or regular non-holy bread and Maaser Sheni food (a portion of your produce taken to Jerusalem to eat) requires that hands be washed with a vessel.
The Talmud presents a statement which contradicts the Mishna in another source. The resolution is one refers to eating and one refers to touching.
The more interesting question is why does eating bread require this seeming stringency where other foods do not require handwashing, meaning one does not have to been in a state of hand purity.
The SD would like to weigh in. We know from the Talmud that in the ancient world people used bread to dip, to convey food from plate to mouth. It seems that bread was like a utensils. One imagines all the Israeli dips that we have at a table and everyone shoving the bread into the dip and then into their mouths. If there hands are dirty, the bread is dirty and then it gets transmitted. In a communal setting this is basic hygiene. But why Maaser Sheni also require washing? My friend Zach Prensky once commented that a farmer in a good year would have lots of produce to Jerusalem for consumption. The farmer and his family could not possibly eat all that food. Therefore they probably invited guests, strangers and poor people to help finish off the food. He imagines a big food party in Jerusalem. A big sharing generous event. It is a communal event where everyone is putting their hands on food. Again a communal setting requiring hygiene.
What is the common thread? Community and sharing. We must eat together . We must enojoy life together. But community requires cleaniness and hygiene.