bpcheckexe appears to be a program or executable (Windows-style name) used for checking or validating backups, boot processes, or system integrity — commonly "bp" can stand for "backup," "boot policy," "bit pattern," or a product-specific prefix. Without additional context, I'll assume it's a utility that performs health checks and verification of backup files or backup processes.
If Suspicious/Malicious:
Here is the critical part. Because bpcheck.exe runs hidden and has a generic name, malware authors sometimes use it as camouflage. The legitimate file is safe, but the fake one is dangerous. bpcheckexe