The official hud.gov website if full of useful information for not only inspector but also residents of the properties being inspected.
Here’s a link to a quick summary in the form of a flyer.
https://www.hud.gov/sites/dfiles/PIH/documents/pih_inspection_resumption_flyer.pdf
You can also find a lot more in-depth information at the link below.
Inspection Information for Residents | HUD.gov / U.S. Department of Housing and Urban Development (HUD)
What is a HUD (or “REAC”) inspection?

HUD provides affordable homes through several rental assistance programs. These programs include public housing, multifamily housing, and housing choice vouchers (Section 8).
These HUD-assisted properties are inspected to make sure they are decent, safe, and sanitary. HUD’s Real Estate Assessment Center (REAC) sets the inspection standards and oversees inspections. These inspections are known as REAC physical inspections.
HUD requires REAC inspections. During an inspection, HUD inspectors check to make sure your property manager or landlord is following HUD’s inspection standards. Inspectors may find issues that your property fix at once to meet HUD’s standards and ensure that your home is decent, safe, and sanitary.
Inspections are meant to help and protect you. Inspectors make sure you are being provided a decent, safe, and sanitary home. They are not there to assess you as a tenant or to check if your home is clean.