Do I need to use JotForms servers or can I still use my own?

what are the benefits of using jotforms servers instead of our current one?  

Please note that JotForm forms are loaded in our servers, all the submission data will also be stored in our data centers.

You can embed the form in your website or you can download and use the form's full source code and have the other resources like the scripts and CSS hosted on your servers, however, there will still be other scripts that will be loaded in our end like the widgets and app integrations. You can get your form's full source code by following this guide: https://www.jotform.com/help/104-How-to-get-the-Full-Source-Code-of-your-Form. 

The main benefit of using just the embed code is that changes you make on the form using the form builder will directly display on the live form. Unlike if you use the form's full source code, it won't do that, you need to actually download the source code again and set it up on your end. Another benefit is that the up-time of the form will always be our priority.  

Using the full source code is only recommended when you want to inject your own custom scripts or functions.

I hope this helps. Do let us know if you have additional questions.