The focal length is the distance (mm) from the sensor to the node point, also known as the point of convergence of the lens.
The longer the focal length is, the narrower the Field of View (FOV) and the shallower the depth of field-- In simpler terms, you zoom in and more background blur
The focal length does NOT affect the exposure. So as long as all three aperture, shutter speed and iso stay the same. The brightness would stay the same
However, keep in mind as the focal length increases the lens would get longer, heavier: and probably more expensive
The diagram below is an amazing material that portrays how the extending focal length causes the FOV to narrow