When the volume and complexity of data began to overwhelm some established approaches, new tools and architectures appeared. That is the practical story behind much of what is called Big Data.
Having a lot of data is not, on its own, proof that a project needs a distributed platform. What matters is the workload: storage, processing, response times, reliability and cost. A relational database may still be the right answer.
Different systems make different trade-offs. Some are well suited to large analytical jobs; others to transactions, documents or searches. The aim is not to replace every older technology but to choose an architecture that addresses a real constraint.
Cloud computing helped make larger infrastructures more accessible. It did not remove the need for engineering judgement. Before adopting a fashionable label, I would rather explain which problem the system must solve and how we will know whether it has solved it.