A Simple Explanation of ZooKeeper in Hadoop
I noticed you are asking several questions related to the Hadoop ecosystem. It is hard to judge how much you know while explaining the things you are asking in a very simplistic manner without knowing that. Might be worthwhile giving some background of what you are trying to understand. But I digress.

Unless you are building an application that requires coordination (think race conditions) you more than likely won't need Zookeeper directly. Many tools within the Hadoop ecosystem do use it for this exact purpose (e.g. HBase).

This is probably the best and most simplistic answer I can give. 


  In a nutshell, ZooKeeper gives you the tools to help build distributed applications. For example, suppose you have a distributed web server application running on 10 nodes. Say, you want to get total real-time hit count. One way to do this is to write an application which connects to the 10 nodes, gets count from each and present the sum. Alternatively, you can have each web server application write their hit counts to ZooKeeper on regular intervals and then query ZooKeeper to get the count.


Source: https://10kloc.wordpress.com/2013/12/21/quick-intro-to-apache-zookeeper/

ZooKeeper Quorum is "A replicated group of servers in the same application is called a quorum, and in replicated mode, all servers in the quorum have copies of the same configuration file."

Source: https://zookeeper.apache.org/doc/r3.1.2/zookeeperStarted.html

A more detailed answer of what Zookeeper is and how it is beneficial can be found on SO (https://stackoverflow.com/questions/3662995/explaining-apache-zookeeper).