The affected user has reached the maximum number of process specified for him into the file /etc/security/limits.conf .
These commands, executed as root, can give you the number of process and of open files for the given user:
ps -U username | wc -l
lsof | grep username | wc -l
To fix the issue increase the NPROC Soft limit according to the user and applications needs; please look at the note below about the /etc/security/limits.conf file.
If third party software is involved, please contact the software vendor to advice about the proper limits to use