PHP can preform calculations - PHP can preform all types of calculations. From figuring out what day it is, or what day of the week March 18, 2046 is, to preforming all different types of mathematical equations.
PHP can collect user information - By this I mean, you can let your user directly interact with the script. This can be something really simple, like collecting the temperature from the user that they want to convert from degrees to another format, or it can be more extensive information, like adding their information to an address book, or letting them post on a forum.
PHP can interact with MySQL databases - And in doing this, the possibilities are endless. You can write users information to the database and you can retrieve information from the database. This allows you to create pages on the fly using the contents of the database. You can even do more complex things like setting up a login system, creating a website search feature, or keep your store's product catalogue and inventory online.
PHP and GD Library can create graphics - You can use PHP to create simple graphics on the fly. You can also use it to edit existing graphics. You might want to do this to resize images, rotate them, or greyscale them. Some practical applications for this are allowing users to edit their avatars or creating CAPTCHA verifications. You can also create dynamic graphics that are always changing, my favorite example being dynamic twitter signatures.
This list of what PHP can do could go on for pages and pages, but if you're new to PHP, hopeful this gives you a taste of the type of things this dynamic language can bring to your website. Want to learn? Start with the beginners tutorial!