Normalize
From Audacity Manual
For a full discussion of the differences between the Amplify and Normalize effects, see this page on the wiki.
Remove any DC offset
When this box is checked Normalize will attempt to remove any DC offset in the selection by finding the average of all the sample values in the selection, then subtracting that average value from all the samples. This works well on long selections containing a mix of sounds, but may actually create DC offset when applied to short sections of recordings of voices or certain instruments that have an inherently asymmetrical waveform.
Normalize Maximum Amplitude to
Enter the value for the maximum amplitude you would like the processed selection to be. Note that you cannot enter positive values: Normalize will not allow you to create clipping.
Difference from the Amplify effect
Normalize processes the left and right channels of a stereo track independently. Amplify applies the same amplification to both channels.
Normalize will not let you create clipping. Amplify will let you create clipping.
Normalize offers the option to remove DC offset. Amplify does not offer this option.
For a more thorough discussion of differences between the Amplify and Normalize effects, see this page in the Audacity wiki