A player in my group is having trouble understanding the concept of dissonant technomancers and what they do differently than regular technomancers or hackers, so how can I explain what dissonance means to him?

Dissonance is to regular Technomancers as Toxic Shamans are to regular Shamans.

Just like the resonance, it's left entirely up to interpretation. Avoid the trap of treaing them as "evil" technomancers.

The thing with the resonance/dissonance, is it's uncertain what it is and what it does and why. Does the dissonace speak to dissonant TM's and corrupt them some-how? Sending them mad? Or do the sociopathic and insane experience the matrix dissonantly?

Basically, you need to have a concept or theory about what the hell the resonance is, before you can try and understand the motivations for an opposing force.

Random speculation, but I like to think of Resonance as finding higher levels of order inside the patterns of data, taking that order and then building upon it; like listening to the music and then by humming along slipping through the shifting sands. Dissonance would be listening to the static and hiss, and then amplifying it, creating a wave of 'corrupted' data which assaults what it comes across. An example of the two would be to think of a pitchfork, one that when struck causes the glass to hum back, the other causing the glass to shatter. And, there's the Tacoma Narrows affect. Anyway, Sir Psycho wrote a neat thing here which I thought was inspiring about the levels of thought on the Matrix...

Resonance, that which technomancers experience while interacting with the Matrix, implies a particular harmony and balance between the Matrix and the technomancer. Dissonance, its polar opposite, implies a discord and break with that equilibrium. Those who rely on this probably leave behind polluted and broken systems. They don't manipulate the Matrix in a graceful way, but rather brutishly bully the Matrix into doing what they want.

IIRC the dissonant otaku "Pax" spoke in Threats 2 about being spoken to by the dissonance, hearing it's voice.

The fact that Pax heard (hears?) voices should be a surprise to no one

I would almost use the real world analogy. People that call themselves hackers and are part of the Free Software Federation would be similar to regular Technomancers. They don't directly want to harm systems and the Matrix. They want to have playful fun and see the endless possibilities on the Matrix (ie no innate criminal intent). Dissonance would be similar to the media version of hackers. People that take pleasure in creating viruses and wrecking systems. They are the type of person that don't care that someone may get hurt or that a company may lose lots of money (in fact they may take pleasure from it).

Resonance and Dissonance could be just two "natural" opposing forces of the matrix, one standing of mantainance of reached equilibrium and the other disruption of said equilibrium; if it were so Resonance would be the force that allowes order to be mantained into the digital sea of information, without it the meaning of information would be lost but an excess of it would froze the system into an andeless loop, while Dissonance would allow to break from existing order, this would allow the system to reach states that otherwise couldn't be reached, on the other hand in excess it would prevent the system to reach any stable state making information uncomprensible to anyone except people deeply attuned to it.
Both of this forces affect deeply the relationship that the technomancer has with the matrix and have a quasi-divine role into the emerged community, potentialy bringing overzelous or psychologicaly unstable subjects to wield harmfull ways: followers of Resonance would be compelled to encode, creating and mantaining programs and data structures, striving to develop the perfect code, an omnicomprensive equation of the matrix, on the oder hand they could grow intollerant toward people that they perceive as bringers chaos to the system, attempting to prevent said people to "harm" the matrix by resorting to various meanings, from pranks to outright violence; as anyone could expect from the polar opposite of the followers of resonance the followers of dissonance reject the notion that the matrix can be represented by an equation or fixed scheme and are compelled to break fixed structures in order to grant the matrix the freedom to express itself for what is at the moment and realize it's potential (thing that changes over time), and their darkside could ranges from rejecting the idea of any degree of order into the matrix to what has been seen with the Ex Pacis.
This vision of the resonance/dissonance relationship would allow the exploration of the interactions of two opposing views of the digital world and would add some deeper concepts compared to a simple dissonace = toxic resonance approach (it would need to twick the rules concerning TMs thought).

just a few thoughts.

Einstein, a Technoshaman shares his perception:
The Resonance is the Matrix Answer to the singing of the Rush Hour, the choir of cellphones being used, the echo of two lovers chatting. Whenever you do something in the so called Real World has a resonance in the Otherworld. Something can be heard by everybody. Most of it is only perceived by our kind.
The dissonance disrupts this harmony, scratches across the soundimage with it's claws and sows sorrow for the sake of sorrow itself. It has no purpose except destruction and entropy. Their existance is not to be allowed.

Obsidian, a former Otaku now E-Scapist palavers about the Resonance and her Counterpart:
It's my mother. Not in a biological sense, but in a digital. It gave birth to my real, surpressed self. I'm grateful for that. And i know that it can give birth to many more if we just make make it stronger and stronger. The matrix is used every day by millions, but that isn't enough. They just use it, switch off their 'link and are done with it. They don't see the fragile world and i can't blame them. It's the human way. But we can overcome our petty programming and have our ascension. Resonance is there to take us in with open arms. There is a world where we can live our dreams, if we would just focus our attention to things that matter!
But the Dark Mirror is hissing around, promising another way, an easier way. It gives power to the weak of mind so they do her dirty work in destroying both worlds. An long dead friend of mine saw some source-to-be. It ain't pretty. But i am not dead yet.