marker.bindPopup(content).openPopup();

marker.updatePopup(newContent);

//marker creation
var marker = L.marker([44.63, 22.65]).bindPopup('something').addTo(map);
marker.openPopup();

//changing the content on mouseover
marker.on('mouseover', function(){
    marker._popup.setContent('something else')
});

$('button').click(function() {
   // Update the contents of the popup
   $(popup._contentNode).html('The new content is much longer so the popup should update how it looks.');

   // Calling _updateLayout to the popup resizes to the new content
   popup._updateLayout();

   // Calling _updatePosition so the popup is centered.
   popup._updatePosition();
   return false;
});