To get your packets to their destination and the replies back to you there needs to be a route there and a route back.
There are two (there are a few other cases as well but we don't need to consider those here) main types of relationships networks have with each other.
In a peering relationship two networks connect to each other so that network A and it's customers can talk to network B and it's customers. Peering connections may run over a direct point to point link or over an Internet exchange point that connects multiple providers.
Different networks have different policies on peering. Pretty much all of them will require you have your own IP space and AS number. Some networks will peer with almost anyone who gets themselves an AS number and buys a link to an Internet exchange point where they have a presence. Some will only peer with networks they see as equals. Some will only peer with you if you build your own international network and peer with them in multiple cities around the world. Some may expect you to pay for the physical connection to them or even pay them for the privilege of peering.
In a transit relationship there is a provider/customer relationship. A transit provider provides a transit customer with connectivity to the Internet in general. The transit provider will almost certainly charge the transit customer money for this service.
At the top of the pile there are a small number of providers who do not buy any transit, relying entirely on peering connections to serve their customers. It's very difficult to join this group as most of the existing transit-free providers are not friendly to new peers.
When you have a small ammount of traffic it's not worth playing the peering game yourself, it's cheaper to pay an ISP to do it for you. As your average traffic needs start to get into the gigabits per second it can make sense to start playing the peering game yourself.