You could do worse than beginning to learn Hadoop; but the Big Data world is more than just Hadoop. Some other technologies you might want to look into, depending on which aspect of this you are most interested in:
Statistics / Probability - the theory behind a lot of the analysis that goes on.
R - data analysis using R often goes hand in hand with the "big data" stuff.
Mahout - a machine learning library, built (mostly) on top of Hadoop.
Incanter - an 'R' like environment written in Clojure
Clojure itself, would not be a bad idea.
Learn about a couple of message passing / message queuing systems: 0MQ, HornetQ, Kafka, etc.
Streaming computation / real (or near) time map reduce: Storm, S4, etc.
On a semi-related note, log collection tools like Flume and Scribe.
A bit about RPC systems and data protocols like Thrift, Protocol Buffers, Etch, etc. wouldn't hurt.
Knowing about some distributed filesystems would be good.. HDFS, and maybe a touch of knowledge about some of the "old school" ones like PVFS.
On the subject of "old school" there is still a place for MPI and OpenMP for solving some types of problems on large clusters. Learning MPI is never a bad thing.
Learning about some modern nosql data stores like maybe HBase, Cassandra, MongoDB, etc. would be good.
Basic Linux sysadmin skills, of course.
Knowing about virtualization technologies: Xen, VirtualBox, KVM, whatever.
Automated deployment / configuration management / remote comand execution tools: Puppet, Chef, cfengine, Fabric, etc.