Why do some accounts on Instagram say "Instagram user"?

An account where you see the text Instagram user is not active. If that account is not active on Instagram for any reason, the name of the account and the content it shares will not be visible.

What exactly does an Instagram user write indicate?

The main reason why someone writes as an Instagram user is that that account is not active. In other words, if the account is inactive in any way, it will say Instagram user.

The reasons why an Instagram user writes may be:

That account is frozen, that is, the account owner freezes it

That account has been closed by its owner

That account has been closed by Instagram

One of the reasons above makes that account say "Instagram user".

Additionally, you cannot see an inactive Instagram account and the posts shared by that account. When you try to log in to the account, you are stuck on a white page and it does not open.

If someone blocks me, will they still write "Instagram user"?

No, it doesn't. When someone blocks you, you cannot find that profile on Instagram at all. Your messages with that person in DM will also automatically disappear.