Some changes to streaming failure docs.

TD gave me the go-ahead to just make these changes:
- Define stateful dstream
- Some minor wording fixes

docs/streaming-programming-guide.md

@@ -286,7 +286,9 @@ For input streams that receive data from the network (that is, subclasses of Net
 Note that, unlike RDDs, the default persistence level of DStreams keeps the data serialized in memory. This is further discussed in the [Performance Tuning](#memory-tuning) section. More information on different persistence levels can be found in [Spark Programming Guide](scala-programming-guide.html#rdd-persistence).
 
 # RDD Checkpointing within DStreams
-DStreams created by stateful operations like `updateStateByKey` require the RDDs in the DStream to be periodically saved to HDFS files for checkpointing. This is because, unless checkpointed, the lineage of operations of the state RDDs can increase indefinitely (since each RDD in the DStream depends on the previous RDD). This leads to two problems - (i) the size of Spark tasks increase proportionally with the RDD lineage leading higher task launch times, (ii) no limit on the amount of recomputation required on failure. Checkpointing RDDs at some interval by writing them to HDFS allows the lineage to be truncated. Note that checkpointing also incurs the cost of saving to HDFS which may cause the corresponding batch to take longer to process. Hence, the interval of checkpointing needs to be set carefully. At small batch sizes (say 1 second), checkpointing every batch may significantly reduce operation throughput. Conversely, checkpointing too slowly causes the lineage and task sizes to grow which may have detrimental effects. Typically, a checkpoint interval of 5 - 10 times of sliding interval of a DStream is good setting to try.
+A _stateful operation_ is one which operates over multiple batches of data. This includes all window-based operations and the `updateStateByKey` operation. Because stateful operations have an infinitely growing lineage, their state must be periodically checkpointed to HDFS.
+
+Checkpointing prevents extra computation during both failure recovery and normal operations by transparently truncating this lineage. Note that checkpointing also incurs the cost of saving to HDFS which may cause the corresponding batch to take longer to process. Hence, the interval of checkpointing needs to be set carefully. At small batch sizes (say 1 second), checkpointing every batch may significantly reduce operation throughput. Conversely, checkpointing too slowly causes the lineage and task sizes to grow which may have detrimental effects. Typically, a checkpoint interval of 5 - 10 times of sliding interval of a DStream is good setting to try.
 
 To enable checkpointing, the developer has to provide the HDFS path to which RDD will be saved. This is done by using
 
@@ -380,15 +382,15 @@ val ssc = new StreamingContext(checkpointDirectory)
 
 On calling `ssc.start()` on this new context, the following steps are taken by the system
 
-1. Schedule the transformations and output operations for all the time steps between the time when the driver failed and when it was restarted. This is also done for those time steps that were scheduled but not processed due to the failure. This will make the system recompute all the intermediate data from the checkpointed RDD files, etc.
+1. Schedule the transformations and output operations for all the time steps between the time when the driver failed and when it last checkpointed. This is also done for those time steps that were previously scheduled but not processed due to the failure. This will make the system recompute all the intermediate data from the checkpointed RDD files, etc.
 1. Restart the network receivers, if any, and continue receiving new data.
 
 In the current _alpha_ release, there are two different failure behaviors based on which input sources are used.
 
 1. _Using HDFS files as input source_ - Since the data is reliably stored on HDFS, all data can re-computed and therefore no data will be lost due to any failure.
-1. _Using any input source that receives data through a network_ - As aforesaid, the received input data is replicated in memory to multiple nodes. Since, all the data in the Spark worker's memory is lost when the Spark driver fails, the past input data will not be accessible and driver recovers. Hence, if stateful and window-based operations are used (like `updateStateByKey`, `window`, `countByValueAndWindow`, etc.), then the intermediate state will not be recovered completely.
+1. _Using any input source that receives data through a network_ - The received input data is replicated in memory to multiple nodes. Since, all the data in the Spark worker's memory is lost when the Spark driver fails, the past input data will not be accessible and driver recovers. Hence, if stateful and window-based operations are used (like `updateStateByKey`, `window`, `countByValueAndWindow`, etc.), then the intermediate state will not be recovered completely.
 
-In future releases, this behaviour will be fixed for all input sources, that is, all data will be recovered irrespective of which input sources are used. Note that for non-stateful transformations like `map`, `count`, and `reduceByKey`, with _all_ input streams, the system, upon restarting, will continue to receive and process new data.
+In future releases, we will support full recoverability for all input sources. Note that for non-stateful transformations like `map`, `count`, and `reduceByKey`, with _all_ input streams, the system, upon restarting, will continue to receive and process new data.
 
 To better understand the behavior of the system under driver failure with a HDFS source, lets consider what will happen with a file input stream Specifically, in the case of the file input stream, it will correctly identify new files that were created while the driver was down and process them in the same way as it would have if the driver had not failed. To explain further in the case of file input stream, we shall use an example. Lets say, files are being generated every second, and a Spark Streaming program reads every new file and output the number of lines in the file. This is what the sequence of outputs would be with and without a driver failure.