There are many solutions to this, The problem is that they may be dated. The answer depends on your server setup, whether you have multisite enabled and if you are on a shared server you may not even have any control over this.

Solution if you have upgraded to Easy Apache 4:

If you are have WHM access you can log in and go to the new tab unser software called MultiPHP INI Editor .  Check the file size of: upload_max_filesize, it is most likely 2M. Change that. You may then be able to upload a larger file but just in case you may want to do two other things. Go to the file wp-config and add this to the top: define (’WP_MEMORY_LIMIT’, ‘256M’); Just below * @package WordPress
*/

If your host has upgraded to Easy Apache 4 you may also have the same options in Cpanel, you may be able to update memory_limit and upload_max_filesize by going to software and clicking on MultiPHP INI Editor. There is also the MultiPHP INI Editor “Editor Mode” along with basic mode. If you think you have tried everything then try this.

Note: I use 256M, it may be to high for you the limit should be considered based on users and the server.

Solution for a fresh install of WordPress

Go to the file wp-config and add this to the top: define (’WP_MEMORY_LIMIT’, ‘256M’); Just below * @package WordPress
*/

See if that works first. You can access that file in the root directory of the wordpress installation. If not then look at some of the other solutions.

Solution for WordPress Multisite

Go to Network Admin->Settings and change the ‘Max upload file size’.

 

Not Recommended but may be used

If you have ftp access or cpanel access then you can pick a folder such as uploads and upload it there. This may work for someone who needs to upload one or a few files but you will need to remember the folder and place a hard url in the editor. If you ever change folders for the installation this may cause errors.

Other places to look:

In WHM you can check under Server configuration in the tweak settings tab, there is a setting there for cPanel PHP max upload size (Minimum: 50; Maximum: 2,047). 

If you have Easy Apache 3 you may want to log into the root account via sftp. There you can download and view your php.ini file.

To verify that it is your php.ini file you can create a file named info.php and put <?php phpinfo(); ?> in it, there you can view limits set by the server.