I’m creating a online store for my website, my aim is to add description to products in home page only how can i achieve it?

You can use is_front_page() function in your code.

add_action('woocommerce_after_shop_loop_item_title', 'description_in_shop_loop_item', 3 );
function description_in_shop_loop_item() {
    global $product;

    if( is_front_page())
    {
        // HERE define the number of words
        $limit = 10;

        $description = $product->get_description(); // Product description
        // or
        // $description = $product->get_short_description(); // Product short description

        // Limit the words length
        if (str_word_count($description, 0) > $limit) {
            $words = str_word_count($description, 2);
            $pos = array_keys($words);
            $excerpt = substr($description, 0, $pos[$limit]) . '...';
        } else {
            $excerpt = $description;
        }

        echo '<p class="description">'.$excerpt.'</p>';
    }
}

Let me know if it is helps to you.

Thank you!