NoSQL databases deliberately give up the relational model's fixed, shared table structure, and in exchange get a data model chosen specifically to fit a particular kind of problem instead. Document databases store each record as a flexible, self-contained document, key-value stores retrieve data through nothing but a single lookup key, and graph databases represent the relationships between records as the primary thing actually being stored, rather than treating those relationships as an afterthought layered on top of separate tables.
A fixed shared schema becomes a genuine constraint for irregular or simple-lookup data
A relational database's fixed table schema requires every record of the same type to share exactly the same structure, which becomes a real, practical constraint when data is naturally irregular, a product catalogue where different product types genuinely have different attributes, for instance, or when an application's primary goal is extremely fast, simple lookup rather than complex relational queries spanning many separate tables at once.
Three genuinely different NoSQL models exist because they solve three genuinely different problems
Document databases suit irregular, self-contained records well, storing each one as a flexible document without forcing every record into an identical shared shape. Key-value stores suit extremely fast, simple lookups, like a session cache, where nothing more complex than retrieving one value by one exact key is ever actually needed. Graph databases suit data where the relationships between records, not just the records themselves, are what genuinely needs to be queried efficiently, a social network's connections being the clearest common example.
What we're still unsure about
That NoSQL databases trade the relational model's shared structure for a model fitted to a specific problem is well established, uncontroversial database engineering. What's genuinely a live, actively debated engineering trade-off is choosing the right NoSQL model, or choosing a relational database instead, for a given real application, since a document database can end up needing relational-style joins reimplemented awkwardly in application code as an application's data grows more genuinely interconnected over time, and predicting in advance whether that will happen for a specific new application remains a real, imperfect judgment call rather than something a fixed rule can settle.
This sits inside NoSQL Models (Document, Key-Value, Graph), one of seven topics in Databases, one of seven domains in Computer Science, one of seventeen subjects the app can quiz you on.