Is the cosmological redshift is a direct measure of the expansion of the universe?
Redshift is a changing of frequency due to the relative motion of an observer and an object. Redshifting occurs when an object is moving away from a stationary observer. This is because the motion of the object away from the observer subtracts from the perceived frequency of the object, making it appear lower than it actually is. Hence, the wavelength is perceived as elongated and shifted towards longer wavelengths.
When discussing the universe and its expansion, observing cosmological redshift is an indication that relative to us as the observers, the universe is expanding away from us. In fact, the universe is expanding locally in every direction at every point in the universe.