It implies that the laundry is already clean (done), but now you are separating it into categories, such as pajamas, work clothes, socks, undergarments, and so on. It's the last step before putting the clothes away.

Your chosen Best Answer has given you a definition of 'sort my laundry', not 'sort THROUGH my laundry'. I don't think that the writer is talking about organising clean clothes to put away after laundering, as the two answers below suggest. The word THROUGH suggests that they are rummaging in a pile or basket of clothes and linens, perhaps in order to find something. Let's say that someone realises that they have absolutely nothing to wear today. So they might sort through their laundry (clothes waiting to be washed) in order to find something which is still clean enough to wear. Or they may have lost something - a lottery ticket, perhaps - and think that it might be in a pocket of a garment that they were wearing last week. They'd then sort through their laundry to see if they could find the lost item. In this second case, it could be either dirty or clean laundry that they're sorting through. Sorting laundry can be one of two tasks : either organising clothes and so on according to their washing requirements before you wash them OR or putting them in different piles ready to be put away after you've washed them. 'Sorting through my laundry' is something different from either of these jobs.

Put Laundry In Piles like towels with towels and pants with pants

Sorting through the laundry means separating the light colored clothes from the dark colored clothes. Separating the delicate clothes or any other clothes that you might want to wash separately. Doing the laundry means washing and drying the clothes.