I read a lot about boundary layer but I don't know exactly what boundary layer is yet.
Airflow (or any fluid flow) will be zero at the surface of the object it's passing over. Imagine the airflow as layers (or "streamlines"), and remember the surface layer velocity is zero. As you move away from the surface, each layer will be going a little faster than the one beneath it until you finally reach "free stream" velocity. All of these low-energy (lower velocity) layers of air between the aircraft surface and the free-stream air make up the boundary layer.
Here is an illustration from NASA:
The boundary layer is the part of the flow near the surface of a body where friction slows down the local flow. Directly at the wall of the body, flow speed is zero and increases the more you move away from that body. The boundary layer ends by definition when the flow has reached 99% of the speed of the outside flow.
An ideal fluid only transmits pressure forces. In reality, air is close to an ideal fluid but not quite, also transmitting shear forces. Those shear forces equalize the flow speed wherever there are speed gradients perpendicular to the flow direction, especially slowing down the flow near the wall. Note that streamwise speed gradients are caused by pressure forces.
At the stagnation point (where the flow hits the body for the first time) the boundary layer thickness is zero, but grows quickly downstream from there. A typical boundary layer thickness at the trailing edge of an airplane's wing is several centimeters.
Growth of a boundary layer on a flat plate (picture source). $v_e$ is the speed of the outside flow (well, 99% of it at the solid blue line), $u$ is the local flow speed and $\tau$ is the local shear stress.
Aerodynamics deals mostly with speed boundary layers, but there are also heat boundary layers, especially in supersonic flow.