What is the difference between osmosis and active transport?

First of all we have to understand that there are concentration gradients between cells and the outside. A higher concentration of solute is when there is more solute (eg salt) dissolved in the solvent (e.g water)- so 10g of salt dissolved in 50ml of water is more concentrated than 5g of salt dissolved in 50ml of water.

Osmosis is the diffusion of water molecules, down the concentration gradient, through a partially permeable membrane.  The water moves fro the area of high concentration of water to low concentration water.

Active transport is the movement of solutes from an area of low concentration to high concentratio so against the concentration gradient. It may help to consider this as the opposite to osmosis. Because you are going against the gradient active transport requires a pump or carrier protein in the cell membrane and therefore energy (made through respiration).