As already answered, what you find in this folder are logs for events or crashes of the Android system. You could open those with a text editor and try to figure things out. All can be safely deleted, but the directory will get populated again as time goes by.
settings put global dropbox_max_files 9
If you are rooted (or via
adb shell - thanks @Irfan Latif) you can issue the command above to limit dropbox files in that dir to 9 (or any other number you prefer). You will only see only latest n events, older get overwritten.
For me, 9 is a good compromise that let me see i.e. latest app crash event, without filling that dir with hundreds of small files. You will not run into any issues by setting that to 0, but you will not be able to see potential errors/crashes (silent or not) in apps that could be worth investigating and fixing.