Cell membranes are composed of what we call a "phospholipid bilayer" composed of phospholipids. Phospholipids have a hydrophillic (‘water loving’) head and a hydrophobic (‘water fearing’) tail. Water can get close to the hydrophillic head while it cannot pass through the hydrophobic tail, thus protecting the cell from foreign substances it does not need. Because of this dual property, the membrane can choose what substances may enter through it and this is what constitutes its semi-permeability.
One of the ways substances can enter through the membrane is through passive transport or diffusion, the movement of substances from higher concentration to lower concentration. This process does not require energy. Substances like oxygen and water easily diffuse through channel proteins when the concentration outside the cell is higher than the inside.