A PCB is rigid board made of multiple layers of fiberglass and copper. It provides mechanical support for components and the electrical connections necessary to create a circuit.
On the surface of a PCB, you'll see exposed copper squares and circles. These are called solder pads and you'll notice some have drill holes through them and some don't. Components that use the drill-holes are called through-hole components whereas those that sit on the pads are called surface mount.
What you won't be able to see are the copper traces that provide conductive paths between the component solder pads. These copper connections allow electricity to flow and snake throughout the board going only where it's needed.
Different devices use different circuit boards, but at a general level the PCB inside a cellphone is the same type of PCB as inside a TV or a computer.
What differs between these devices are the components on the PCB and the routes between them. That's where a PCB designer comes in.