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In layman terms, devices that can connect to internet and can transmit data points to remote server or receive instructions from remote server for performing some actions are termed as Things. The capability to interact with other remote Things or Servers over the Internet make these devices smarter and bring in a new era of connectedness called Internet of Things.
There is no specific definition of Cloud, since Cloud is just a set of services available over internet in the form of IaaS, PaaS or SaaS offerings. All major Cloud vendors provide storage as a service which is infinitely (virtually) scalable and available with a guaranteed SLA. However, going by the context of the question, answer to these questions will make sense: How to store IoT data on Cloud, in what form and how to retrieve such data?
Let’s keep this short: Data that does not fit into conventional DBMS or similar storage due to either/all of these challenges: sheer volume, velocity or lack of definite structure, processing and analysis of which could require massive distributed compute, storage, etc. can be termed as BigData.