Use wp_enqueue_scripts, not wp_print_styles?

Everywhere is said that you need to use wp_enqueue_scripts() instead of wp_print_styles().
wp_print_styles() is located in wp-includes/functions.wp-styles.php.

So what does it mean? What should I change? Where? Why? Can it compromise my theme?

In short, as of WordPress 3.3 use wp_enqueue_scripts to load JS and CSS. wp_print_styles has/had some minor bugs with it (namely, it may include your scripts in the admin as well) – here and here are some more details on all of that. It doesn’t sound like there’s any major security flaws or theme breaking here, just better practice to use wp_enqueue_scripts.

Additionally:

• wp_enqueue_scripts – for enqueuing on the front end
• login_enqueue_scripts – for enqueuing on the login page
• admin_enqueue_scripts – for enqueuing on admin pages