More specific details would be nice & helpful since we don't know what OS you are using nor which update you are referring.
Try booting into Safe Mode to see if the updates will install. If this works it usually means you have some third party software installed that is interfering with the normal operation of macOS (typically anti-virus apps, cleaning apps, or third party security software).
If you were having other issues before the update issues and Safe Mode does not solve your current update issues, then you may still have an issue with third party software or you may have a hardware issue such as a bad hard drive. If so, then run the Apple Diagnostics to see if any hardware issues are detected. Also run DriveDx and EtreCheck making sure to post both reports here using the "Additional Text" icon which looks like a piece of paper.