From the abstract of Google’s MapReduce research publication page:
MapReduce is a programming model and
an associated implementation for
processing and generating large data
sets. Users specify a map function
that processes a key/value pair to
generate a set of intermediate
key/value pairs, and a reduce function
that merges all intermediate values
associated with the same intermediate
key.
The advantage of MapReduce is that the processing can be performed in parallel on multiple processing nodes (multiple servers) so it is a system that can scale very well.
Since it’s based from the functional programming model, the map and reduce steps each do not have any side-effects (the state and results from each subsection of a map process does not depend on another), so the data set being mapped and reduced can each be separated over multiple processing nodes.
Joel’s Can Your Programming Language Do This? piece discusses how understanding functional programming was essential in Google to come up with MapReduce, which powers its search engine. It’s a very good read if you’re unfamiliar with functional programming and how it allows scalable code.
See also: Wikipedia: MapReduce
Related question: Please explain mapreduce simply