file.js

var Parent = mongoose.model('Parent', parentSchema);
var parent = new Parent({ children: [{ name: 'Matt' }, { name: 'Sarah' }] })
parent.children[0].name = 'Matthew';

// `parent.children[0].save()` is a no-op, it triggers middleware but
// does **not** actually save the subdocument. You need to save the parent
// doc.
parent.save(callback);