Just add the following snippet in you non-WP page:
// This is so that we can use WP functions
Now you can call wp_get_recent_posts to get the latests posts.
But reading your question agin, it seems that you are NOT using Wordpress, but you want a function similar to wordpress? In that case, you're in the wrong forum. You should ask it over at StackExchange.
And if you are not using WP, then you need to fill in more details. Are you using any CMS? IS you site custom PHP? Storing data in DB? And so on.