MapReduce is a framework that provides high performance in solving problems in a parallel way of computers, servers, clusters...
Here there is an interesting presentation about NoSQL and MapReduce: http://www.slideshare.net/j_singh/nosql-and-mapreduce
And here a popular NoSQL Databases web page: http://nosql-database.org/
The CAP theorem says that, for a distributed system, it is impossible to simultaneously provide the following guarantees:
- Partition tolerance