Complex sentence: If the sampling theorem is not satisfied then the resulting digital signal will have aliasing and to ensure that the sampling theorem is satisfied a low-pass filter is used as an anti-aliasing filter to reduce the bandwidth of the signal "before" the signal is downsampled.
Split into simpler sentences: If the sampling theorem is not satisfied then the resulting digital signal will have aliasing. To ensure that the sampling theorem is satisfied, a low-pass filter is used as an anti-aliasing filter to reduce the bandwidth of the signal "before" the signal is downsampled.