DC offsets are voltages which DON'T move (except manually), but which can be added to another voltage via an adder or similar module to change that signal's voltage level.
Going back to the matrix mixer example...let's say you've got a sequencer line that you want to transpose. So, the CV from that would go into one of the matrix inputs. And from there, let's send that over to row #4. Now, with the offset jumper (on the backside of the module) in place, NOT connecting inputs will cause the matrix mixer to have a DC offset signal on...we'll call it input row #2.
So, if you want different pitches, you use different DC offsets and the matrix mixer combines those with the incoming CV. In bipolar mode (pot centers are "0", and you've got positive mixing to the right, negative mixing to the left), you have attenuverter-like functions. Meaning, that if you want to drop the sequencer's pitch by...we'll say an octave...it would look like this:
Sequencer CV -> Matrix input 1
No connection to input 2, which makes that an offset source
Now, using the vertical mixer row 4...turn up "row 4, input pot 1" to full to let the CV in, then adjust "row 4, input pot 2"...which is the DC offset level...so that you now have the same signal, but one octave down. If you send the CV to row 3 now, then raise the input to full but NO offset, this will give you the sequencer CV MINUS the offset. At that point, just use a two-input switch (actually, the best one for the task is Doepfer's A-151, as the input can be switched between 2, 3 and 4 inputs) and then by switching back and forth between row 3 (pure CV) and row 4 (-1v added to CV), you've got that octave jump...you just need to figure out when you want those octave shifts (via the A-151) to happen. DC offsets are very useful for shifting signal levels by exact amounts, in other words.
One other point, though...DC that gets out of the modular CAN be big trouble if you connect the synth to a DC-coupled amp. Speakers don't do well with that...to the point that you can actually set the speaker drivers ON FIRE by sending a big DC signal into the amp...which puts the speaker into "full travel" while majorly overheating the speaker coil. Not good. This is why I tend to insist on output modules that can DC-isolate, as those will NOT pass an accidental DC offset that's made it to the output stage. Plus, they do a good job of stopping trash, noise, etc from getting into the modular by accident from the signal outputs.
That's a decent overview, I think...it's not a concept that verbalizes well; you really need to see what it does hands-on.