When molecules cannot move easily enough through the plasma membrane, facilitated diffusion occurs. Molecules cannot pass through the phospholipid bilayer of the plasma membrane easily when particles are either charged or polar.
Facilitated diffusion is a form of passive transport which does NOT require energy. Passive transport occurs when molecules go down the concentration gradient.
A concentration gradient is when particles or solutes move from a highly concentrated area of particles to a less concentrated area of particles. This process is aided by proteins located on the plasma membrane (membrane proteins) such as transport proteins: Channel proteins and carrier proteins.
Channel proteins are laid throughout the membrane to provide a Hydrophilic passage through for the molecules to avoid the Hydrophobic core (Hydrophobic means to avoid polar substances such as water. Hence the terms hydro-water and Phobic think of phobia, fear of something. While Hydrophilic is the opposite and attracts water). An example of a channel protein is Aquaporins which allow water (polar H20) to diffuse through the membrane. Aquaporins are essential for plant cells, red blood cells, etc.
Nerve and muscle cells have gated ion channel proteins to enable the flow of charged ions such as sodium and potassium present in the sodium potassium pump of action potentials. These charged ions, like Na+ and K-, need channel proteins in order to move through the membrane. This creates a polarized membrane, and it helps with the action potential (you'll learn more about this later. If you're confused, don't worry too much. Just remember this concept is used in nerve cells). If a signal such as an electrical signal is activated these channels open their gate to transmit these signals through cells.
Carrier proteins alter their shape to allow the flow of molecules through the concentration gradient of the membrane similarly to an enzyme substrate complex. Their rate of transport is slower than that of channel proteins. Carrier proteins provide an easy way for hydrophilic molecules to pass through the concentration gradient.
Active transport is used when the substance is moving in the opposite direction than its natural tendency would take it. The substance is transported to a region of higher concentration from lower concentration. Because it's against nature (like riding a bike uphill), it requires the use of ATP.
This is well demonstrated with the sodium-potassium pump. It takes out three sodium ions into the cell and brings in two potassium ions. Because both ions are moving against nature, ATP is needed. This is primary active transport.
Image Courtesy of Hyperphysics
But there is something called secondary active transport. In this transport system, something is actively transported by using energy from another substance going through the membrane through simple diffusion. This of it as a mom with a stroller going through a door. Let's say the baby 👶 going through the door is active transport. The baby alone going through the door would need a lot of energy, it can't go on its own. But the mom, on the other hand, was already going through the door through simple diffusion. So the mom's "momentum" is used to push the baby through the door as well.