"Dirty memory" is memory which has been changed somehow - that's memory which the garbage collector has to look at, and then decide what to do with it. Depending on how you build your data structures, you could cause the garbage collector to mark a lot of memory as dirty, having each garbage collection cycle take longer than required. Keeping this number low means your program will run faster, and will be less likely to experience noticeable garbage collection pauses. For most people, this is not really a concern.
"Resident memory" is memory which is currently loaded into RAM - memory which is actually being used. While your application may require that a lot of different items be tracked in memory, it may only require a small subset be accessible at any point in time. Keeping this number low means your application has lower loading times, plays well with others, and reduces the risk you'll run out of memory and crash as your application is running. This is probably the number you should be paying attention to, most of the time.
"Virtual memory" is the total amount of data that your application is keeping track of at any point in time. This number is different from what is in active use (what's being used is marked as "Resident memory") - the system will keep data that's tracked but not used by your application somewhere other than actual memory. It might, for example, save it to disk.
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