Most probably the file is just being cached by the server. You could either disable cache (but remember to enable it when the site goes live), or modify href of your link tag, so the server will not load it from cache.
If your page is created dynamically by some language like php, you could add some variable at the end of the href value, like:
<link rel="stylesheet" type="text/css" href="css/yourStyles.css?<?php echo time(); ?>" />
That will add the current timestamp on the end of a file path, so it will always be unique and never loaded from cache.
If your page is static, you have to manage those variables yourself, so use something like:
<link rel="stylesheet" type="text/css" href="css/yourStyles.css?version=1" />
after doing some changes in the file content, change version=1 to version=2 and so on.
If you wish to disable the cache from caching css files, refer to your server type documentation (it's done differently on apache, IIS, nginx etc.) or ask/search for a question on https://serverfault.com/
Assuming IIS - adding the key under <system.webServer> with the right settings in the root or the relevant folder does the trick.
<?xml version="1.0" encoding="UTF-8"?>
<configuration>
<system.webServer>
<caching enabled="false" enableKernelCache="false" /> <!-- This one -->
</system.webServer>
</configuration>
That said sometimes one still has to recycle the Application Pool to "bump" the CSS. Therefore: Disabling IIS caching alone is not a 100% guaranteed solution.
For the browser: There are some notes on fine-grain controlling the local cache on FF over on SuperUser for the interested.
