Each person you ask "What is an IoT cloud server?" will likely give you a different answer. A whole lot of marketing goes into making you gravitate towards certain solutions that may not be optimal for your requirements. Many IoT solutions have modest requirements and do not need to run on expensive to rent services. In addition, many of these expensive solutions use less than optimal software products when communicating with memory constrained edge nodes, such as mbed powered devices.
What if you could setup your own secure IoT cloud server for only $8 a year, a server that can handle up to 10,000 connected IoT edge nodes, where each communication link is protected by state of the art encryption? If this sounds interesting, check out the secure IoT recipe at the following page (tutorials listed at end of page).
https://makoserver.net/smq-broker/
The tutorials include instructions on how to set up your own mbed board as a secure edge node.
The following video shows how a device can be controlled from a web browser in real time by using the IoT protocol. The Cloud Server acts as a broker for the communication between the browser and the device.