As an extension to @JBNizet's answer for more technical users here's what implementation of org.w3c.dom.Node interface in com.sun.org.apache.xerces.internal.dom.ParentNode looks like, gives you the idea how it actually works. 
public void normalize() {
    // No need to normalize if already normalized.
    if (isNormalized()) {
        return;
    }
    if (needsSyncChildren()) {
        synchronizeChildren();
    }
    ChildNode kid;
    for (kid = firstChild; kid != null; kid = kid.nextSibling) {
         kid.normalize();
    }
    isNormalized(true);
}
It traverses all the nodes recursively and calls kid.normalize()
This mechanism is overridden in org.apache.xerces.dom.ElementImpl 
public void normalize() {
     // No need to normalize if already normalized.
     if (isNormalized()) {
         return;
     }
     if (needsSyncChildren()) {
         synchronizeChildren();
     }
     ChildNode kid, next;
     for (kid = firstChild; kid != null; kid = next) {
         next = kid.nextSibling;
         // If kid is a text node, we need to check for one of two
         // conditions:
         //   1) There is an adjacent text node
         //   2) There is no adjacent text node, but kid is
         //      an empty text node.
         if ( kid.getNodeType() == Node.TEXT_NODE )
         {
             // If an adjacent text node, merge it with kid
             if ( next!=null && next.getNodeType() == Node.TEXT_NODE )
             {
                 ((Text)kid).appendData(next.getNodeValue());
                 removeChild( next );
                 next = kid; // Don't advance; there might be another.
             }
             else
             {
                 // If kid is empty, remove it
                 if ( kid.getNodeValue() == null || kid.getNodeValue().length() == 0 ) {
                     removeChild( kid );
                 }
             }
         }
         // Otherwise it might be an Element, which is handled recursively
         else if (kid.getNodeType() == Node.ELEMENT_NODE) {
             kid.normalize();
         }
     }
     // We must also normalize all of the attributes
     if ( attributes!=null )
     {
         for( int i=0; i<attributes.getLength(); ++i )
         {
             Node attr = attributes.item(i);
             attr.normalize();
         }
     }
    // changed() will have occurred when the removeChild() was done,
    // so does not have to be reissued.
     isNormalized(true);
 } 
Hope this saves you some time.