That "thing" on your screen is a kernel panic report. (It is not a Terminal window even though it superficially resembles one.)
That usually means that some file that loaded at startup time is either damaged or not compatible with the rest of the OS. That prevents the boot process from completing so the only thing the computer can do without a fully function OS to tell you what happened is to display that report.
When it occurs early in the boot process immediately after an OS update has been applied it usually means a third party "kext" (kernel extension) file is the culprit. Typically this is because the developer either hasn't yet updated the file to be fully compatible with the OS update or you haven't yet installed the latest version that is.
It can also mean that a preexisting part of the OS that the update doesn't replace was damaged for some reason. This is often a part that is rarely used (for instance only during the update process itself) so there is no sign of the damage until the update reveals it.
Unless the problem is in an essential part of the OS, a safe boot will at least get the Mac booted but with limited functionality. This will allow you to do some troubleshooting & possibly fix it, for instance by manually downloading & running the combo version of the update, which contains more replacement files than the 'delta' version Software Update will install. That has a better chance of replacing any damaged OS files, but won't do anything useful if the problem is an incompatible or damaged third party file.