Incrementing and displaying a field if not empty
$vidnum = 'video_';



Presumably $vidnum is short for $video_number, but this isn't a video number.  It's the prefix before the video number.  

     $video_number_prefix = 'video_';


You can go ahead and call it what it is.  


     for($n=0; $n&lt;=9; $n++) {
     $next = $vidnum.($n +1 );



You say that you have ten fields but you write 9.  There are two ways to write it with 10.  

     for ( $n = 0; $n &lt; 10; $n++ ) {


But the second works better with your $next variable, which I'm going to rename to $video_identifier.  

     for ( $i = 1; $i &lt;= 10; $i++ ) {
         $video_identifier = 'video_' . $i;


You don't need to save the value of the string literal.  You only use it once, so you can just use it.  

Starting with 1 instead of 0 means that you don't have to add 1 to the value before using it.  

I switched from $n to $i, as $i is a more common loop iteration variable.  


     $video = get_field('' . $next . '');



This seems more complicated than it needs to be.  

         $video = get_field($video_identifier);


Adding the empty strings doesn't seem to accomplish anything.  


         if (!empty($video))
             echo '&lt;div class="video ' . $next . '"&gt;' . $video . '&lt;/div&gt;';



The single statement version of an if is harder to read and maintain.  

         if ( ! empty($video) ) {
             echo '&lt;div class="video ' . $video_identifier . '"&gt;' . $video . '&lt;/div&gt;' . "\n";
         }


I also added a line break at the end.  Functionally this won't matter, but it makes the HTML easier to read.  

The whole thing:

&lt;?php
     for ( $i = 1; $i &lt;= 10; $i++ ) {
         $video_identifier = 'video_' . $i;
         $video = get_field($video_identifier);
         if ( ! empty($video) ) {
             echo '&lt;div class="video ' . $video_identifier . '"&gt;' . $video . '&lt;/div&gt;' . "\n";
         }
     }
?&gt;


This also fixes your indentation issues.  

Note that I'm not commenting on your use of get_field.  Looking at the documentation, it seems that get_field depends heavily on the configuration.  Without the configuration, that is off-topic for review.