A quick refactor to make the render method idempotent:

MyView.js

var MyView = Backbone.View.extend({
  
  initialize: function() {
    
    //el inserted to the page on init, only called once
    $('#content').append(this.el);
    
    this.model.on('change', this.render, this);
  },
  
  render: function() {
    //.append() changed to .html(), which replaces instead of stacks content
    this.$el.html( /* some HTML */ ); 
  }
  
});
 
new MyView().render();