The Jews (also known as the Judeans or the Israelites) just heard about how Jesus is the "bread of life" and how believing in him results in food resulting in everlasting life. But they didn't buy into that. They doubted that Jesus came from heaven because Joseph gave birth to Jesus (6:42). It's worth noting that although Jesus had a birth on Earth, he was still sent by God, as seen from the various feats Jesus did (that even the Judeans saw). Not to mention that his birth is a bit different from the typical birth.
However, Jesus told them to not murmur (6:43) -- especially since Jesus would explain things a bit more.
First off, Jesus talks about how no one has the ability to come to Jesus without having the Father drawing him (6:44). In particular, Jesus talks about how the people who heard and learned from the Father comes to Jesus, as cited by Isaiah (6:45-46). In other words, the Judeans need to count on the Father in order to be further convinced by Jesus -- especially in the teaching and drawing department.
Jesus officially established the role in which the Father plays in helping us believe in Jesus. Later on, Jesus will talk about how the Father draws everyone (though not everyone is receptive). For those who aren't convinced on believing in Jesus, I'd recommend keeping an open mind regarding Jesus and the Father because the Father teaches and guides people to Jesus.