In traditional networking, you have literally to be connected to a network to have access to it - either with an ethernet cable or via Wi-Fi.
You connect to the Internet via a router/modem provided by your ISP - any device on your home network when it access the internet will be identifiable as coming from that router/modems public IP address.
Your ISP will be able to see your internet traffic - even using HTTPS it's still possible to see what websites you are visiting etc.
A VPN is a way of connecting into another network as if you were directly linked to it. It is possible to route some or all of your outbound traffic to via the VPN-connected network. I use VPN access for a number of things:
1) Obscuring my real IP address from the websites I visit
2) Preventing my ISP from inspecting my traffic
3) Ensuring that when I'm using a public Wi-Fi connection, my network traffic isn't inspected/manipulated
4) Using self-hosted services which run on my home server when I'm away from home
5) Remote administration of servers and network appliances for work
1-4 are mainly privacy centred. As I've become more aware of how our data is collected and analysed, I've become less reliant and cloud services and more reliant on my own self-hosted services. Unfortunately I can't eradicate them from my life entirely - because work, but at least I can obscure some of my on-line footprint.
My personal recommendation is BlackVPN. I don't actually use them, but I have friends that do and I intend to switch at some convenient point in the not to distant future. For years I've used PIA and, well, they are based in America which doesn't sit well with me.
One of my main reasons for running a pfSense firewall instead of just relying on my ISP provided routers is so that multiple devices can share the same VPN connections - their internet connections round-robbined between them so one HTTP request will go via Toronto and the next New Zealand etc. ...it doesn't play too well with sites that use GeoIP functionality but I generally try and avoid them anyway, or sites that see access from multiple IP addresses in parts of the world as potential hacking threats, but it doesn't generally cause me a problem.
This is a useful insight:
https://www.socialcooling.com/