A local server is a computer that serves a client within the local network or LAN. That means that in most cases, it will not be connected to the internet. If it is connected to the internet, it will typically be protected with a password so not everybody can access its services.
A local server is like a shed in your backyard.
You have your main house that people can see. Anyone can walk by and knock on your front door. However, they cannot go into your backyard and access your shed, it is not open to the public.
The services your shed offers are only for you and those that you let access it.
A local server is a server that is for private use only.
If you don't have a product yet, then this term isn't much value to you. Go on with your day!
A local server still isn't too valuable to know when your product is live as 99% of the time, you will be accessing your product via the cloud. Your developers may use a local server to test the product or you may use a local server if there is some high proprietary and confidential reason to do so, but by majority you should be set.