Thank you so much for your answer! The examples really help a lot! So if I'm understand correctly, partitioning is comparable to diffusion (substance moving from areas with a high concentration to areas with a low concentration, until its more or less evened out), but generally includes this substance moving from one phase or material to another?
To give some more details about the exact problem they've given us, it's about metal contamination of a floodplain system. A river passes by a brick factory and transports metals such as copper and zinc, then drops them off downstream as sediments. There, the metals mix into the soil solution and contaminate the area, impacting the health of local plants and wildlife. They also go into how these metals can bind into the soil in different ways, e.g. under aerobic and anaerobic circumstances, and how these all affect the resulting toxicity, but this I don't fully understand yet.
Where solid-solution partitioning comes into play is here:
"For the risk assessment of contaminated soils, information on the solid–solution partitioning and speciation of contaminant metals is necessary as they both affect metal mobility and bioavailability." I believe they want us to understand how it impacts concentrations of copper and zinc, soil toxicity, and consequently the system as a whole.