Translation: You can make money by doing dirty jobs.
Conversely, those involved in dirty jobs are likely to be wealthy.
This is is an expression originating in northern England, and you have to say it with a Northern accent. That is to say, "Moock" not "Muh-ck" and "Br-ass", not "Br-arse".
Brass (it rhymes with lass) is a slang word for money. It's used almost exclusively in Yorkshire and Lancashire.
I'm told it comes from the 16th century, when most money was still in the form of gold pieces, but brass was beginning to come into common usage. Brass, being of a similar colour to gold, was used to mimic real currency, and so the word came to mean money, but with a connotation of having something fake about it. Well, that's what I found from the web, and it sounds plausible enough to reproduce here. if you can find a better explanation, I'm only too willing to hear it.
Incidentally, words related to brass suggest cheap, tacky or gaudy. Brazen (the correct word for something made with brass) has come to mean bare-faced, flagrant or audacious. Brassy means cheap and showy.
But that's an aside. If you talk to a northerner — well, if you spoke to a northerner 50 years ago, and asked if he had the brass, then he would know perfectly well that you were asking if he had enough money.
Muck is a northern word for anything dirty: coal, mud, sewage and suchlike. It's a gross generalisation, but in general, people don't like to do jobs involving dirt. That being the case, for those few who are prepared to work in and with the muck, there are others willing to pay them to do it.
Hence the dual meaning of the phrase. First, if you want to make money, then consider cleaning sewers, or sweeping chimneys.
Second, and this is the more common usage: Do not be surprised if the local sewage contractor is wealthier than the local jeweller.
In this context the phrase is offered as a compliment:
Upon seeing the local drainage contractor buy a new, high-specification Lexus, one observer might say to another, in an approving tone, "where there's muck, there's brass."
That is to say, 'good for him: he might be doing a dirty job, but he gets well-paid for it.'
Conversely, when the same person has a blocked drain that has been cleared by the same contractor, he might utter the same phrase, but in somewhat less complimentary tones: "where there's muck, there's brass." This time it means "Gosh, it might be a dirty job, but he charges a lot for it and I resent having to pay so much. If the job were not so dirty I might think about doing it myself."
In a third meaning, when a youngster is seeking employment, a parent might suggest a job at the sewage farm. Upon hearing the youngster's cries of distress, the parent might comment, in worldy-wise tones, "where there's muck, there's brass." This time, the meaning is, 'if you want to earn good money, try doing the jobs that others do not want to do.'
Hazelnut says: I suppose it also applies to aspiring criminal lawyers. After all, a good defence solicitor can make quite a packet keeping "Fingers" McNulty or his mates out of the nick.