It's the number of files being monitored by Splunk for that monitor/batch data input. When you setup a data input via file/directory monitoring (and restart if deploying data input via conf files), Splunk creates a list of files that it should be watching/monitoring for changes and the column "Number of files" represent that.
This is what one would assume but it is definitely not the whole case. I would open a support case and also ask them to update the docs on this because it does different things for different types of inputs. For example, the Splunk_TA_nix has an input for
/var/log/secure and this screen shows a value of
144 even though it only contains the exact file and 4 rotated files. This makes no sense.
I don't think there is 100% accurate method to know exact number of files being monitored. The inaccuracies are generally due to whitelist/blacklist regex. You can also compare the numbers from UI (the place you mentioned), from CLI (Run $Splunk_Home/bin/splunk list monitor ). The UI is actually uses Rest API Endpoint
/data/input/monitor/<<URLENcodedMonitoredPath>> to get that info. See this for more info on that Rest API Endpoint.