In Germany, I hear a lot of jokes containing "Deine Mudda", but I don't understand them. What does this mean and what kind of jokes are containing them?
Deine Mudda is just an intentionally misspelled
Deine Mutter (your mother) to phonetically mimic the pronunciation of this phrase by a low-educated street bully.
Joking viciously about your mother is an indirect way to insult you: if your mother is so bad, you seem to be even worse.
The typical jokes include some negative comparisons of somebody's mother with some illustrative example, following the form "`Deine Mudda ist so ... dass sie (sogar) ...". Those comparisons are usually very funny and make the overall joke sound not so dirty or insulting, but rather elicite some laughing and smiling.
Deine Mudda ist so dick, sie sitzt sogar im Stehen.
Your mother is so fat that she is sitting while she is standing.
Deine Mudda ist so dick, dass wenn sie sich wiegt, steht auf Waage ihre Handynummer.
You mother is so fat that when she stands the scale displays her cell number.
Deine Mutter ist so fett sie legte sich an den Strand und Greenpeace schmiss sie ins Meer!
Your mother is so fat that when she was lying on a beach Greenpeace threw her into the water.
Deine Mudda ist so dumm, dass sie in Mario nach links läuft.
Your mother is so stupid that she runs leftwards in Mario.
These jokes are also common in English (and probably originate from English language), but are rather limited to the mother being fat. Here are some examples:
Your Mom is so fat she sells shade in the summer.
Your Mom is so fat that when she walked by the TV I missed three episodes.
In addition to Alexander's answer, I would like to add that simply replying "Deine Mudda!" means something like "Get lost!". Of course, as with all youth slang, usage probably varies highly by region and even social circle.
This is shortened from a form of exchange often seen among adolescents:
"Du schuldest mir noch zehn Euro." - "Deine Mutter schuldet Dir noch zehn Euro!"
This means something along the lines of "Yes, I understand; don't bother me!" (Or "I disagree with your statement"). It is obviously not a nice thing to say, but often used as a form of bantering among friends.
There are some regional variants. In bavaria, for instance, I've heard the variant "Dei' Mudda", which is "Deine Mutter" in bavarian dialect.
"Deine Mudda", pronounced like Hamburg slang, is used nationwide, though, probably popularized by hip-hop artists. There is a big and influential hip-hop scene in Hamburg. Of note, there was a 1999 Single by Hamburg hip-hop stars Fünf Sterne Deluxe named "Ja, ja... deine Mudder" which reached position 38 in the german single charts. The record label was called "Yo Mama Records"...