Redis is not a drop-in replacement for an SQL server. It's more like a RAM based key value store with better data type options than "just string" and it's also like a swiss army knife. In a generic Rails/Laravel/MVC setup you could use redis to handle one or all of: sessions, cache, queue, pubsub, (probably more), effectively lifting the burden from your SQL server.
I believe if you think of Redis as a data structure server, then there are lots of applications you can build out that have simple commands like set and get for both lists and hashmaps that are slightly different ways of thinking about saving and retrieving your data. The concept of a set is very powerful and easier to implement I believe than using SQL.
Your data, eventually? If that's OK, some of the time, then Redis might be fine and will be much faster (since not losing data involves much more work).