The Nostr client you are using sends a deletion request note (kind 5) referencing the note you want to have deleted to all of your write relays. If the relay is configured to respect deletion requests (they are not required to do so), the note will be deleted from those relays. However, it is very likely already propagated to other relays that your deletion request did not get sent out to, so the note probably still exists and is viewable by others.

This is because there are relays that aggregate notes from other known relays, even though you aren't intentionally writing to them. There's not really anything you can do to prevent this, just like you can't prevent someone from screenshotting your post on legacy social media platforms. The best we have are lockbox relays, which flag notes that should not be rebroadcast to other relays or aggregated by other relays using a "-" tag, but even that does not have to be followed by other relays. If the note exists and is readable anywhere, it can be copied to other locations.

Whenever you post on Nostr, you should assume that the note will exist somewhere on some relay forever, even if you request deletion.