Pixelation results from high levels of data compression in video files. The compression makes video files smaller, cutting memory usage, but too much compression hurts the video quality. After this data is gone you can't get it back. The video file no longer "remembers" any more detail in the pixelated areas. You can take some steps to clean up the video, but you cannot restore full sharpness and clarity.
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Check out the original video file, if you have access to it. It might not be compressed at all. In that case, just save a new copy with a lower level of compression or a different file type or encoding codec; or, if practical, create an unmodified copy of the original. If you have no access to a higher-quality version of the video, then you will have to try and clean up the pixelated video.
Load the pixelated video into a video-editing program.
Check the program for any filters or tools that provide you with options for cleaning up "pixelation" or "mosaic" noise and apply them. Play around with these options to see what settings yield the best results.
Look into other video-editing software if you are not satisfied with the results. More expensive software often contains more powerful tools. However, keep in mind that no software can truly replace the lost picture data.