Why did I have to restart my router to install programs

I have had a Windows 11 PC for 6 months. Recently, it wouldn't install any programs. It would run Chrome, but wouldn't run games that needed updates to play. Installing other programs like Firefox failed. The files downloaded, but installing them failed. I then wiped the PC and the remained. I have a Windows 10 PC and had the same issue. At that point I thought it must be the router and restarted it, and everything is working again. I use Windows Defender and turned off the firewall. I don't understand what was happening and would like to know why I couldn't install programs and why the router

Question by aneuroo on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.