Editing speech is a matter of combining different words by isolating, cutting, copying, or pasting. You must retain the natural rhythm of the way the words are said (cadence) and also be careful not to cut off any word or even breath.

Editing music is much more complicated than editing speech.  Rather than cutting up one element you have to cut a composite of many elements.  What may be a good edit point for a vocal may not work with other instruments.

Editing music requires an understanding of rhythm and arrangement.  You must edit music so that the passing rhythm is uninterrupted or the edit will be noticed.  Your edit points must be the precise (the end of the each piece must fit perfectly to the beginning of the next piece).

Although it is recommended that you edit music at either downbeats or strong drum hits, sometimes in order to allow a melodic element to start or finish a statement you must edit in an unusual place, such as a beat before the downbeat.  A nice way to accomplish this is to line up your 2 sound clips on adjacent tracks so that the down beats are synchronized, then finding a good place not on the downbeat to cut and cutting at exactly the same point in the timeline.

When editing spoken word with no rhythmic foundation (such as editing a speech rather than editing a sung vocal), there is great freedom.  Not only can the audio be edited to change the content that is spoken (to re-write the script) but also spaces between words and sentences can be changed to alter emphasis.