Repro, reprocessing, and reprocessed
In the CIAO documentation we use the terms repro, reprocessing and reprocessed to mean one of:
the chandra_repro script (or equivalent) has been run on a Chandra observation to ensure that the latest calibration products and suggested algorithms have been applied (that is, a user has used the CIAO tools to apply the latest corrections to the data);
the Chandra data archive - or a significant fraction of it - has been re-run through an updated version of Standard Data Processing (that is, the Chandra software and archive teams have re-run the software).
Unlike some telescope archives, such as Hubble, the Chandra archives do not re-process data when you request it from the archive (so called on-the-fly reprocessing). Instead, the calibration files (CALDB) are updated when needed, and the user can re-apply them using CIAO (this is case a above).
Occasionally it becomes necessary to reprocess the archive, because the changes require data products not available to users. This is case b. At the time of writing (May 2013), the last reprocessing run was Repro IV.
The current processing status, and history, of an observation can be found from the Chandra Observations Processing Status page. For ObsId 1843, Figure 1 of the Introduction to the Data Products thread shows the status as of May 2013.
The note on processing versions thread shows you how you can find out what version of the SDP was used by the archive to process your data.