To 'normalize' is to adjust the volume so that the loudest peak is equal to (or a percentage of) the maximum signal that can be used in digital audio. Usually you normalize files to 100% as the last stage in production to make it the loudest possible without distortion. Another reason to normalize is to have multiple tracks sound equally loud, or to have equal average loudness.
The 'Peak' normalization method finds the sample of the greatest magnitude within the file. Normalization is then done with this value as the peak. With the Normalize Peak Level set to 100% (0dB), the whole file will be amplified so that the peak reaches 0dB.
The 'Average Loudness (RMS)' normalization method normalizes according to the file's average loudness, or volume. Multiple files normalized to the same peak level using this method will have equal average loudness. The 'Normalize Peak Level' for this method should be set much lower than for the Peak method, because the average loudness will always be lower than the peak sample.
The 'Peak Loudness (RMS)' normalization method attempts to normalize according to how loud the loudest part of the file will sound. This is the best method to use to make multiple tracks sound equally loud. As with Average Loudness, the 'Normalize Peak Level' for this method should be set lower than for the Peak method, because the peak loudness is lower than the peak sample. The actual algorithm used takes the RMS of each 50ms window in the file, ranks the windows from loudest to quietest, and then takes the 95th percentile of these as the 'peak'. Note that no adjustment is made for humans' differing perception of different frequencies.
The Perceived Loudness (dBA) normalization method uses A-weighted decibels which is an expression of the relative loudness of sounds in air as perceived by the human ear. Normalization is made because the human ear is less sensitive at low audio frequencies, especially below 1000 Hz, than at high audio frequencies.
The Integrated Loudness (EBU) normalization method uses the R-128, an international standard for loudness normalisation and maximum level of audio signals. Several platforms use this such as Spotify (-14dB), YouTube (-14dB), Apple Music (-16dB), Facebook (-18dB), and TV / Radio (-23dB). See EBU R-128 for more details.