A mesh topology is one in which A device on the network can ask another device to pass a message along to the hub. It doesn’t have to talk to the hub directly.
The SmartThings hub is a plastic box that contains multiple devices. One is a certified Z wave controller. Another is a certified zigbee controller using the zigbee home automation profile (ZHA). A third lets the hub use your ethernet connection to talk to your SmartThings cloud account.
The SmartThings cloud can also use the Internet to talk to other clouds, such as IFTTT or Logitech Harmony or Lutron or Nest.
So in your own home, the SmartThings hub establishes two different mesh networks, one for Z wave and one for Zigbee. The responses from the devices on those two networks are collected by the hub and sent up to the SmartThings cloud account which decides what to do with them.
This is why when you have SmartThings you can turn on a zwave switch and have a zigbee smart bulb turn on. The Z wave switch talks to the Z wave controller inside the SmartThings hub. The hub sends a message to the cloud account. The cloud account has the logic that understands that when that switch is pressed, the zigbee bulb should be told to come on. The cloud sends a message to the hub to that effect. The zigbee coordinator inside the hub at your house then sends a message to that particular smart bulb to turn on. Zigbee devices and Z wave devices don’t talk to each other, but each can talk to the hub and hub can talk to the cloud account where everything gets sorted out.
And, yes, that’s a long chain to get a message sent and introduces multiple potential points of failure, but it all works pretty well and pretty quickly and gives you a tremendous amount of flexibility in exactly what devices you can add to your account, which is what people like about SmartThings.
The same basic process is used for any protocol that can be integrated with SmartThings. One way or another, a message gets to your cloud account, The logic runs to decide what message should then be sent to a device in your home, and one way or another that message then gets sent to that device.
For Z wave and zigbee devices, The smartthings hub in your home handles the “last mile” of the message delivery. For cloud to cloud integrations, SmartThings sends a message to the other cloud, and the other cloud uses the Internet to send the message to the individual device at your house.
But the specifics of each message path are invisible to the individual customer, from the customer’s point of view, the SmartThings account just handles everything.
Also note that the official SmartLighting feature is able to do some “local processing” for some specific devices, which means the messages don’t have to get sent to the cloud account to be interpreted, there’s a processor inside the hub which will figure it out. But most of SmartThings is still Cloud based. For example, the mobile app on your phone will not be able to talk to your hub unless Internet is available, even if the phone is on your own Wi-Fi network. The messages still have to be processed in the cloud.