Hadoop is a a framework that allows for the distributed processing of large data sets across clusters of computers using simple programming models.
There are four main modules in Hadoop.
Hadoop Common: The common utilities that support the other Hadoop modules.
Hadoop Distributed File System (HDFS™): A distributed file system that provides high-throughput access to application data.
Hadoop YARN: A framework for job scheduling and cluster resource management.
Hadoop MapReduce: A YARN-based system for parallel processing of large data sets.
Before going further, Let's note that we have three different types of data.
Structured: Structured data has strong schema and schema will be checked during write & read operation. e.g. Data in RDBMS systems like Oracle, MySQL Server etc.
Unstructured: Data does not have any structure and it can be any form - Web server logs, E-Mail, Images etc.
Semi-structured: Data is not strictly structured but have some structure. e.g. XML files.
Depending on type of data to be processed, we have to choose right technology.
Some more projects, which are part of Hadoop:
HBase™: A scalable, distributed database that supports structured data storage for large tables.
Hive™: A data warehouse infrastructure that provides data summarization and ad-hoc querying.
Pig™: A high-level data-flow language and execution framework for parallel computation.
Hive Vs PIG comparison can be found at this article and my other post at this SE question.
HBASE won't replace Map Reduce. HBase is scalable distributed database & Map Reduce is programming model for distributed processing of data. Map Reduce may act on data in HBASE in processing.
You can use HIVE/HBASE for structured/semi-structured data and process it with Hadoop Map Reduce
You can use SQOOP to import structured data from traditional RDBMS database Oracle, SQL Server etc and process it with Hadoop Map Reduce
You can use FLUME for processing Un-structured data and process with Hadoop Map Reduce
Have a look at: Hadoop Use Cases.
Hive should be used for analytical querying of data collected over a period of time. e.g Calculate trends, summarize website logs but it can't be used for real time queries.
HBase fits for real-time querying of Big Data. Facebook use it for messaging and real-time analytics.
PIG can be used to construct dataflows, run a scheduled jobs, crunch big volumes of data, aggregate/summarize it and store into relation database systems. Good for ad-hoc analysis.
Hive can be used for ad-hoc data analysis but it can't support all un-structured data formats unlike PIG.