There are two categories of cellular transport: passive transport and active transport. In passive transport, the cell doesn't use any energy to facilitate the motion of particles from one location to another. Instead, the cell relies on the tendency of high energy configurations to transpose into low energy configurations. Particles or molecules tend to move randomly from areas of high concentrations to areas of low concentrations (i.e. diffusion). Diffusion continues until an equilibrium is reached. Other examples of passive transport include facilitated diffusion, and osmosis.
Facilitated diffusion involves the diffusion of specific particles through transport proteins found in the cell membrane. Osmosis is the physical phenomenon where water diffuses through a selectively permeable membrane. In both these cases, motion is still from areas of high concentration to areas of low concentration.
Active transport involves the cell expending energy to move a particle from a low energy configuration to a high energy configuration. Particles or molecules are actively moved where they are needed. Examples of active transport include protein pumps, endocytosis, and exocytosis. A protein pump can change its shape to move a protein from outside to inside the cell. This requires energy. In endocytosis, the cell morphs its shape around the particle and envelops it. This also requires energy. Exocytosis forces material out of the cell into the bulk. Here, the cell again changes its shape to accomplish the motion.
There are two types of cellular transport - Passive and Active transport. Passive transport does not require any energy from the cell, and includes diffusion,osmosis (osmosis is the diffusion of water), and facilitated diffusion. Active transport does require energy from the cell, and includes protein pumps, endocytosis, exocitosis. In diffusion, molecules move from the side of high concentration to the side of low concentration. In facilitated diffusion, molecules move the same way, except they pass through proteins. In active transport, molecules move from areas of low concentration to areas of high concentration, requiring energy. The following videos are excellent for illustrating the different processes: