1st Reason - If you just installed a business central VM (using this wizard). It installs a self-signed certificate. When I try to download symbols on my laptop, I get the "could not download symbols" error. The VSCode output window shows the following details
Error: The SSL connection could not be established, see inner exception.
The remote certificate is invalid according to the validation procedure.This error occurs because the VM is installed with a self signed certificate. For development and testing purposes this is just fine. The quickest and easiest solution is to download the certificate and install it on your local laptop (i.e. trusting the certificate). Note, you should only do this if you trust the VM you are connecting to. Below are some links that walk you through doing just that.
For macs, follow the instructions under Add Certificate To Trusted Authority here
For windows, use the instructions here
Note that if you like working in a RDP session, you won't see this issue. The error occurs only if you run VSCode on your laptop and try connecting to the server.
2nd Reason - Recently I ran into another reason why you can get this error. If the server you connect to has, say version 16.x.x.x and your app.json "application" property is set to version 20.x.x.x then you get this error because the server doesn't have the version you are requesting. Change the version in app.json. Look at your .alpackage folder. Sometimes it is able to download the system package which has the version x number installed on your BC installation.
3rd Reason - If you have a multi-server install then your Business Central server is on a different machine than your web server (IIS) (on-prem scenario). In this case the URL for the BC server is different from the URL used by the browser. Make sure the URL in launch.json is the URL for the BC server not the IIS server. Also make sure you have the port property set correctly.