This error is related to security software, spyware or a virus preventing the 'SteamNew.exe' file from being overwritten during the update process.
1. Check your security software's settings
If you are running an antivirus program, firewall program, or any security product, these may interfere with the deletion and replacement of the 'SteamNew.exe' file. Please check your settings for the program and make sure that you are prompted to allow activities which may trigger the security software.
2. Disable any programs which interfere with Steam
Make sure any programs that may interefere with the process are either disabled or uninstalled. You can find a list of programs that may interfere with the update process at https://support.steampowered.com/kb_article.php?ref=9828-SFLZ-9289
3. Remove Spyware, Adware, and Viruses
If the issue persists it is possible that a virus, adware, or spyware may be interfering with the installation process. Please go to https://support.steampowered.com/kb_article.php?ref=6057-YLBN-1660 for more information on removing the offending program.