When you need more than one server to run your database.
The main different between NoSQL/SQL DBMS is about auto scaling. NoSQL scales well on multiple servers, as they were designed to work that way, while SQL dbs do not.
agreed in spirit, but politely disagree in practice, at least in the context of an absolute statement. auto scaling data stores can be sql or nosql based, and there is a ton of nosql data stores that have no concept of autoscaling at all.
while there is many big platforms out there that have big nosql solutions that are autoscaled, there is probably way more that are sql based. companies such as Facebook and Twitter were using large scale sql data stores.
auto scaling is also a tricky word. as it can mean many things. possibly you mean how things like riak and mongo can automatically scale out without having to write code to do it. certainly nothing prevents folks from doing this with any data store. and there is utilities like Twitter gizzard, tumblr jet pants, and YouTube vitess that help.
often in my experience by the time you get to the point of needing a database that can scale itself your use case and production needs often demand a very well understood data model and flow. often it's easy to shoot yourself in the foot worrying about that early on. auto scaling can be an expensive mistake that can lead to even more technical debt and monetary debt too.
The main different between NoSQL/SQL DBMS is about auto scaling. NoSQL scales well on multiple servers, as they were designed to work that way, while SQL dbs do not.