Processing a string containing product variants
This code is not very easy to follow. 

(I am going to assume that the variables $search_db_row['variations'] and $variation where previously initialized)

Firstly, Your spacing is not very clear: 
This way:

$variations = explode("|", $search_db_row['variations']);

foreach ($variations as $variations_arr1) {
    $variations_arr1_exp = explode("-", $variations_arr1);
    $variations_arr[$variations_arr1_exp[0]][] = $variations_arr1_exp[1];
}

foreach ($variations_arr as $variations_arr2k =&gt; $variations_arr2v) {
   $variation.= $variations_arr2k.": ";
   foreach ($variations_arr2v as $variations_arr2_value) {
      $variation.= mb_strtolower($variations_arr2_value, "utf-8").", ";
   }
}


makes it easier to see what is connected to what.

Secondly, consider changing the variable names.
Something like this:

$initial_variations = explode("|", $search_db_row['variations']);

foreach ($initial_variations as $initial_variations) {
    $each_variation = explode("-", $initial_variations);
    $variations_arr[$each_variation[0]][] = $each_variation[1];
}

foreach ($variations_arr as $variation_types =&gt; $variations_values) {
   $variation.= $variations_types.": ";
   foreach ($variations_values as $variations_value) {
      $variation.= mb_strtolower($variations_value, "utf-8").", ";
   }
}


Makes it easier to follow because the variable names themselves tell me what is happening. 

As far as reducing the code/getting rid of the foreach's, you could try like this:

foreach ($initial_variations as $initial_variations) {
    $each_variation = explode("-", $initial_variations);
    if ($previous_type != $each_variation[0]){
        $variation .= $each_variation[0].": ";
    }
    $variation .= mb_strtolower($each_variation[1], "utf-8").", ";
    $previous_type = $each_variation[0];
}


two more points (homework): 


you have a trailing comma at the end of each group (this prints Size: xs, xl, Color: red, green, instead of Size: xs, xl Color: red, green)
this could use a comment (or two)