ACID and NoSQL are not mutually exclusive, although that is a common misconception due to the fact that almost all NoSQL databases gave up ACID in exchange for BASE (eventual consistency), making the development of their distributed databases much easier. However, ACID is simply a set of properties that allows you to group a set of reads & writes to a database into a transaction that is Atomic, Consistent, Isolated, and Durable. That set of reads & writes does not need to be SQL - in our case, it is a set of reads from and writes to a database of ordered keys and values.

For example, you could read the values associated with keys "a" and "b" and "c" and based on that information, make a change to the values associated with keys "c" and "d" and then commit the transaction. The transaction then either fails completely (if one of the keys you read had been written to since your read, in which case you re-try the transaction) or succeeds completely. That is an ACID transaction in a (NoSQL) key-value store.