How to create a category Landing Page without using views Module

I hope code below helps you with your issue.

function get_terms(){

$vocabulary = taxonomy_vocabulary_machine_name_load(YOUR_TAXONOMY_MACHINE_NAME); // put it in quotes

// passing vid of taxonomy through 'taxonomy_get_tree' function to get all terms belong to it
$terms = taxonomy_get_tree($vocabulary->vid);

$term = array();
foreach($terms as $value){ // iterate through each term

$term = taxonomy_term_load($value->tid); // pass tid to get term object

$title = $term->name;
$description = $term->description;

}
}