Integrations in HACS (or custom_components as they are often referred to) are community-built integrations.
When you download, update or remove an integration in HACS, you need to restart Home Assistant.
There is 1 exception to this:
If the integration supports configuration with
config_flow, you do not have to restart Home Assistant after the download.
You can go straight to the "Configuration" section of the UI, then to "Integrations".
You may need to clear your browser cache before you see it in the "+" list.
Note that this only applies for the initial download of that Integration, if you update it, you still need to restart Home Assistant before it loads the new files.
Any Integration you download with HACS is stored in
custom_components/ in your Home Assistant configuration directory.