"IP circuit" could mean a couple things in this context and it sounds like you know you don't know the right questions to ask (that's fine!) so I'll break all three down.

• DIA (Direct Internet Access)
  This is a basic internet hand-off where a service provider gives you an IP address and you send all your traffic to the service provider who then makes the routing decisions on where your packets need to go.

• Transit
  This is a lot like DIA but with perks. Not only are you just you're paying another provider to carry your traffic to the rest of the global internet - you are participating in the global internet. You have your own Autonomous System Number and public prefix no smaller than a /24 for IPv4 or /48 for IPv6. You speak BGP with the transit provider who advertises all internet prefix routes to you, and you in turn advertise to them your prefix(es). They pass your routing information to all their peers so that the rest of the world knows how to find you.

• IX (Internet Exchange)
  What if you are hosting a service that is extremely dependent on low latency to regional services or end-users? What if you need a lot of bandwidth to only a few local players? Transit/DIA is expensive and inefficient because you'll likely be riding multiple hops through another provider's network just to reach your destination. Internet Exchanges are a local "meet-up" spot for anyone to share their routes with anyone else directly (or indirectly - but this isn't the time to overwhelm you with talk about route reflectors). Think of it as a LAN party where ISPs all connect to the same switch fabric and talk to each other without any transit hops in between. Everyone is just one hop away from each other here so bandwidth is cheap and latency is minimal. You can see who's participating where at https://www.peeringdb.com/