Selenium doesn't speak English
A webpage looks different to a computer than to a human (and if you are computer, you can skip this blog post). Most humans don't care how computers look at web pages, but it may matter to you. That's because if you are writing a Selenium test, you have to know how to see a web page the way a computer does. A webpage has things on it. The text you're reading now isn't a blog post to a computer - it's a thing in a webpage. So are all the links and buttons on this page. If you were writing a Selenium test that wanted to come to this page and check for text, that would be easy; you just need to know the URL for the page and the text to look for. If you wanted to write a test that came to this page and clicked on a button, that would be more difficult. You'd need to know how to tell the computer which button to click on. That's what XPath is for. It stands for "XML path"; XML is (loosely) the language your page is written in, and path means the path to an element (in this case a button) in the page.
XPath leads to the spot
Everything in the page is an element. Most of them live inside another element. The code for an element looks like this:
<type>content</type>. "Type" is what kind of element it is; input, paragraph, division (of the page), etc. Where you see
<type> is where the element's code begins, and
</type> is where it ends. The content in the middle is some combination of text that is going to appear in the webpage and lists of other elements. Those elements can contain other elements. When you're looking at a page, those elements are visible as rectangles, with backgrounds or images or text in them. They live inside bigger rectangles that partition up the page. Those rectangles probably live inside even bigger rectangles. The "path" to an element is the list of elements it lives inside. To construct one, you list all the elements it lives inside, starting with the top one. You can also do fancier things, like scan the whole page for certain kinds of elements, or some specific kind of element but only when it's inside another certain kind of element. It wouldn't make sense for me to explain how to write an XPath here, because w3schools has XPath Syntax covered.
Don't use XPath
There are two important things to say about XPath with regards to Selenium. First, XPaths are only one of three ways to tell Selenium how to locate an element, and it's the worst one. Second, that if you must use XPath locators, there are some steps you should take to keep them from breaking or slowing the script down when they're being used. They're the worst kind of selector to use because of their brittleness and their slowness. If you can, you should use unique id attributes on the elements you're trying to interact with through Selenium. If that fails, you should try to use CSS selectors.
If you have to use XPath, be careful
If you must use XPaths, you have to make a tradeoff between reliability and speed. A fast xpath might say "click on the third input element in the second div in the fourth paragraph in the body element of the html element." It's like having a treasure map that says "Turn left at the first fork in the path, then right, then your third left." That's easy to follow, but if someone adds another fork to the trail anywhere along that path, those directions will lead somewhere else. An XPath like that will be interpreted quickly by Selenium, but it will stop working as soon as you put another div along the path through the page. A more reliable XPath might say "I want you to find an element that is an input element inside any paragraph inside any element that is inside any div as long as it has a 'name' attribute of 'blah' ." It's like a treasure map that says "You want the spot between two pine trees that are 100 feet to the west of an oak tree that's just after a left turn in the trail." Those directions will stand the test of time, but when you need to follow them, you'll have to check every left turn, every oak tree, and every pine tree on the island to be sure. This is less brittle, but it will force the browser to check a lot more things on the page before it can be sure it has found what you want.