Yes, you really can talk all over the world using a small radio (HT) that will fit in your shirt pocket. This is typically done by using a repeater that is connected to the Internet. You can talk to anyone within range of the repeater without using the Internet link, but if you want to talk to someone on the other side of the world, just punch in the correct code and you are linked to that repeater.
Another way of reaching out is to have what is called a micro-node in your home or car. It functions like a small, short range repeater that is connected to the Internet through your computer or a tiny computer called a Raspberry Pi. Micro-nodes are very handy when traveling or any time you are out of range of an Internet-connected computer.