Hosting your application let you free from the burden of load of back up and security measures, since by hosting your application you are making your host providers responsible for securing the server and backup. This let you save cost as you need not worry about buying or leasing the equipments to run the third party applications or spend additional capital on training of your staff or consulting. You can utilize your manpower in your on-going development projects and other work because your staff will be free from that extra responsibility.
The hosting provider are also liable for backing up and restoring the applications in the event of a disaster and manage the server effectively and in addition they provide you technical Support, security management of servers, which also saves in equipment and consulting costs and gives you an free feeling of additional work knowing your applications are being backed up and taken care by someone.