When you use WordPress to design your website, you have a number of template options to choose from. The standard WordPress install comes with the latest default theme and possibly a few historical ones. You can then chose to download a theme from the WordPress site or from third party sites. Some of the themes are free and others you will have to pay for.
When choosing your theme, it is important to understand which ones are mobile compatible and in what way. You need to try a responsive theme that will adapt automatically to the screen size of the user regardless of if it is a tablet / mobile or a 20 inch screen on a computer. This will allow your website to still look its best and most importantly to still function the way it should to all your visitors. You can chose to download a pluggin to create a mobile version of your site, which you may choose to do, but even if you do decide to do this, you should still make sure that your theme is responsive. Trying to adapt an old theme to be responsive can be tricky and often it is better to start again with a more up to date theme.