Active transport is similar to diffusion, in that it is the movement of molecules. However, whereas diffusion occurs passively and molecules move from an area of high concentration to an area of low concentration, active transport reverses this. Molecules are transported from an area of high concentration to an area of low concentration, and this requires energy in the form of ATP.
Active transport accross a membrane takes place via specific transport proteins. ATP produced in respiration causes these proteins to change their 3D shape when a molecule binds with it, so that it is taken into the cell/transported from the cell against the concentration gradient. An analogy of a kissing gate can be used.
So, for example, if the concentration of mineral salts inside a root hair cell is higher than that outside the cell in the soil, then diffusion cannot take place passively as the concentration gradient is not in the right direction. Mineral salts would not passively move from an area of low concentration (soil) into an area of high concentration (cell). In this case, active transport must be employed for the cell to absorb the ions in the soil. They bind to proteins on the cell membrane, which actively "carry" them into the cell using energy from respiration. In this way, the plant can absorb the mineral salts even though the passive diffusion gradient is the wrong way.
Active transport can be defined as "the energy consuming transport of molecules or ions across a membrane against a concentration gradient, made possible by transferring energy from respiration."