I have some difficulty with this concept as well, but I can try.
Osmotic pressure = MRT where M is molarity (mols solute/L solution), R is gas constant, and T is temperature (K). As you mentioned, water tends to move from low solute concentration to high solute concentration (diluting the solute wherever it is). Osmotic pressure is simply the pressure the solute particles exert back when water flows into a compartment containing the solute particles (which cannot flow into the compartment of pure water) for example. You see the relationship between osmotic pressure and molarity in the equation above; the greater concentration/molarity of particles you have, the greater the osmotic pressure they exert.
I think a capillary example illustrates this particularly well. In a capillary, filtration (fluid flowing from the blood stream to the interstitial space (ISF space)) generally predominates on the arterial end. Absorption (fluid flowing from ISF space to the blood stream) predominates on the venous end. Why is this? Basically, you have a balance of forces/pressures governing which end filters and which end absorbs.
Pressures:
1) Capillary hydrostatic pressure - generated by pumping heart which pushes the blood through capillaries. This favors filtration into the ISF space.
2) Capillary osmotic pressure - pressure exerted by interstitial fluid solute particles to push fluid back into blood stream.
3) Interstitial fluid osmotic pressure - pressure exerted by plasma protein/solute particles to push fluid into the ISF space.
The hydrostatic pressure is greater on arterial end than the capillary osmotic pressure; the ISF osmotic pressure is small on both ends and doesn't affect the overall balance significantly. This tilts balance in favor of filtration (fluid flows into ISF).
The hydrostatic pressure is smaller on venous end than the capillary osmotic pressure; again ISF osmotic pressure is not significant here. This tilts balance in favor of absorption (fluid flows into bloodstream). Problems occur when this natural balance goes awry (clot forms in the venous end -> increase in hydrostatic pressure on end that should have small hydrostatic pressure -> increased filtration and possible edema.)
So basic principle: Increased concentration of particles = increased osmotic pressure (which makes sense since more particles = more force/pressure on the compartment walls).
If anyone sees something wrong with this description, please feel free to correct me. Hope that helps!