A short code is a five to six digit code rather than the ten digit phone number you are familiar with.  Since it is short the number is easily remembered and helps to increase response rates.  Most companies are on a shared shortcode such 57682 the retailer or director is identified by their unique keyword.  A keyword is exclusively used for your business.   A customer will send your keyword as the message to the shortcode.  The keyword acts like a trigger telling the system to send a message back to the customer.  You will have created the message ahead of time and as customers text in they receive  the message you created. 

SMS is 100% opt-in. It is against mobile marketing Association rules to send unsolicited messages.  When a customer sends a text message to the shortcode 57682 with your keyword as the message they are joining your list.  If you want your database to grow then include your keyword and shortcode on marketing materials in store signage such as receipts posters and table tents are a great place to start