The overlap of 50 % means that with a transformation from the frequency to the time domain and a reverse transformation from the time to the frequency domain, the reproduced signal deviates from the original signal. Only by partial consideration of the previous and following block a reproduction is possible and the artifacts of the codec are omitted.
The MDCT transformation is used, among other things, in Advanced Audio Coding( AAC), where it works with two different block lengths. The long blocks are based on 2,048 samples, the short ones on 256 samples. This technique achieves a higher frequency and time resolution in AAC compression compared to MP3.