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It is a system that lets any devices that are connected to internet to comunicate with each other without human-to-human or human-to-devices interactions. For example, an airconditioner than can be switch on and off via smartphone, or the motion sensor that would swich on the light in your office.
It is the "second layer" or an off-chain of payment protocol that operates on top of a blockchain. Payments on this network do not need block confirmation and it will be instant.
It is number of transactions done per second. For example, there are 10 transactions of Bitcoin done in 1-minute. The TPS would be 10 transactions/60 seconds = ~0.17 TPS.
