The Muddy Hand is a disembodied hand made covered with mud that appears in one of Rodrick's horror movies entitled "Hello, You're Dead". In it, the Muddy Hand travels the countryside looking for victims to strangle, and the last person who sees it is always the next victim. The film in question frightened Rowley and Greg at the end (where the Muddy Hand strangles its last victim and walks straight at the screen, implying that the viewer will be its next victim.) This made Greg and Rowley become really paranoid that the Muddy Hand was out to get them (despite being a fictional character.) Greg then figures out that since it is just a hand it would take a long time to get to them so they stopped worrying about it. It was only mentioned in Dog Days. In Rodrick Rules, The Foot is used (which is most likely a parody of the Muddy Hand).
In Fregley's version in Dog Days film,in the wilderness awareness he tells a campfirestory about the Muddy Hand. It is about an old woodsman who chops of his own hand by mistake while chopping wood in rain,his hand is the Muddy Hand.
The Muddy Hand looks just like an ordinary hand,the only notable difference is that the hand is quite dirty and has black spots that resemble mud, which is the reason why it's called the "Muddy Hand". It's also unknown how he kills its victim, it most likely strangles the victim.
If the Muddy Hand was not in the book, the plot could have been very different, as Greg and/or Rowley, in specific scenes, would not have been scared and would not have taken the plot-defining actions (such as Rowley smashing Greg's hand with a hammer because he thought it was the Muddy Hand.)
Hello You're Dead cover, the movie where the hand comes from.