How to synchronize my Drupal site with content pulled from a Wordpress site?
Wordpress exports its content using RSS.  The standard way of pulling this content on a regular basis is to configure the core RSS Aggregator module (disabled by default) to pull the content from the WordPress RSS.  It is highly configurable, you can pull daily or by the hour.
Here is a link to an introduction to the Drupal Aggregator - quoting:

Aggregator is a key part of Drupal that is often ignored.
I blame it on the confusing name. No, Aggregator is not an animal in Florida that eats people. Aggregator is a module that imports content from RSS feeds into Drupal.
Because it has a name starting with &quot;A&quot;, Aggregator is the first module that people ever see on the Modules page. In this tutorial, we're going to show you what Aggregator does and how to use it.