How do you explain leaving a job on a resume?

It is not required to carry the reason for leaving a Job on a Resume. These are aspects which can be taken up if asked during the face to face interaction or if inquired specifically during a telephonic interaction.
 
A professional should be ready with a decent reply to the question and should ensure that the same does not in any way be critical of the earlier employer or management or superiors. If the profile has been stable over a period of time exploring new opportunities is understandable and one can mention that they are looking to go up the corporate ladder and or that they are looking to bag a better offer both in terms of profile and remuneration.
 
If for some reason there is a lack of stability in the profile then one need to be ready to answer some tough questions. For example if you took up an offer with a Start-Up and the company closed down and you lost the job. A possible explanation could be a decent reason to take up the offer like the credentials of the promoters or the area of work or the Branding or the offer being too tempting to let go. One can then admit that there was a lapse in decision making and what seemed initially to be very interesting did not work out the same and in hindsight that it was a flawed decision making or a mistake!