A checksum is a short sequence of letters and/or numbers generated from the contents of a file by HJSplit or another program. If two files are exactly the same, the checksum of those files are also exactly the same.
On the other hand, the checksums of two files being exactly equal does not guarantee 100% that these files are equal. One can just say that these two files have a high likelyhood of being equal when their checksums are equal.
Now what is the use of a checksum?
Suppose you split a large file, sent the split parts to a friend, who joins the files. But when the friend tries to open or run the file, he/she gets an error message and the file will not be opened. What can be the cause? Very likely the file has been corrupted during download or during the process of sending email. To find out whether file-corruption is the actual cause, generate a checksum of the original file, and have your friend generate a checksum of the joined file.
If both checksums are equal, it is likely (but not absolutely sure) that the two files (original file and joined file) are equal. If the checksums are not equal, it is certain that the files are not the same.