A telephone network is much like a road network. It is a series of routes connected to each other so that traffic can reach its destination. Smaller routes lead from homes and businesses until they get to an interchange, where they join larger routes, which allow for more traffic to move more quickly. That, in essence, is how a telephone network is organized. Worldwide telecommunications is this process on a global scale.
The smaller roads in this analogy are the copper cables that connect homes and businesses to the network. They all link up at an exchange, which acts like the interchange and joins them up to the core network. The core network is the highway, allowing much more traffic to travel much further, much faster.
Highways sometimes lead to borders, like those of Canada and Mexico. Here the traffic has to be checked, passports verified, and sometimes inspected before being allowed on its way. The same happens with worldwide telecommunications traffic. The same as roads have their border crossings, so does a network.
There are points in every network called interconnects. These are the equivalent of border crossings, where traffic from one network meets another. If the traffic needs to cross the "border" between networks it is inspected, verified, noted, and passed along. These interconnects are what allows network traffic to connect everyone, wherever in the world they might be.
Just about every city, state, and country has interconnects with their various telecommunications companies. Each will have agreements with the other about how they handle traffic, how much they charge for it, and how quickly it will get to its destination. This is why long distance calls often cost more. Not only does the telephone company have to pay for the equipment that carries the call, it also has to pay the other carriers for using their network to let the call reach its destination.
At each interconnect, the traffic is inspected; this is how the telephone companies know how much to charge each other for using their network. Much like a passport inspection, the traffic is checked, its origins verified, and records kept to the company can be billed. This happens at every interconnect across the world.
Worldwide telecommunications is a complicated field that involves a lot of equipment and many contracts, agreements, and co-operation between countries and companies. This is all essential for users to be able to connect with anyone, anywhere, and is what makes telecommunications a universal entity. Worldwide telecommunications is a cooperative effort by all the different companies, governments, and other bodies enabling these interconnects.