Why do I need to trust the relay operator? With what am I entrusting them? Is there a document that explains at least the basics of what Amthest is doing / wants me to do?
Can I give you some home work? Your first step is the figure out which relays you would like to store your content. There are many options and the most important part is to know who the operator is and trust that person. Nos.lol and nostr.mom are run by nostr:nprofile1qqsflmrj64um42nh9tu7w8nr3dffy9tjrt8xururype9ajle7alctvgppemhxue69uhkummn9ekx7mp0qyg8wumn8ghj7mn0wd68ytnddakj7qg4waehxw309ahx7um5wghx77r5wghxgetk9uukdx2g. Nostr.band is run by nostr:nprofile1qqs99d9qw67th0wr5xh05de4s9k0wjvnkxudkgptq8yg83vtulad30gpz9mhxue69uhkummnw3ezuamfdejj7zx57ul. Nostr.wine by nostr:nprofile1qqsrmpp2lmx4u2fl9zmxy7fnwp9rlwxwz5a2j8tep2c376n494z2gtgpz9mhxue69uhkummnw3ezuamfdejj7qgcwaehxw309anxjmr5v4ezumn0wd68ytnhd9hx2tcprpmhxue69uhkxun9v968ytnwdaehgu3wwa5kuef09lplkt. Nostr.band by nostr:nprofile1qqsrx4k7vxeev3unrn5ty9qt9w4cxlsgzrqw752mh6fduqjgqs9chhgpzamhxue69uhhyetvv9ujuurjd9kkzmpwdejhgtcpz4mhxue69uhhyetvv9ujuerpd46hxtnfduhszyrhwden5te0dehhxarj9ekk7mf0mpwca6, etc. You can also put your own relay up with nostr1.com from nostr:nprofile1qqs8eseg5zxak2hal8umuaa7laxgxjyll9uhyxp86c522shn9gj8crspz9mhxue69uhkummnw3ezuamfdejj7qgjwaehxw309ahx7um5wgerztnrdakj7qgkwaehxw309a3x2an09ehx7um5wgcjucm0d5hsvlnggv. Lots of options but the more you know the better it gets.
Discussion
Because they are the ones hosting your content and can moderate you anytime they want. On Nostr, you control your keys. But the content is managed by relays, either by you or by operators. And you need to trust them to keep your content and not track you and your follows.