in dictionary of lenru, the "amato" word(which means beloved), is built by am + at + o. I searched in suffixes of esperanto, but I didn't find anything about -at- suffix. so what does it do?
The suffix -at denotes the passive present tense participle: someone or something who/which is currently influenced by the action of the root. Here you have the noun (-o), which are taken to mean humans if otherwise not indicated, so the amato is the person who is loved or in short beloved.
Take a look at the grammar section of the participles at the site Lernu. (Note, you can change the language of the page at the bottom right.)
The -at- suffix is the present passive participle. When used with -o, it signifies a person that is having an action done to them. So in this case an amato is someone that is being loved. A serĉato would be someone that is being searched for.
Note that the a in -ato is the same as the a in the present tense suffix -as. This isn’t a coincidence. In fact, you can use the other two tenses in a similar way. For example trovito woud be someone that has been found (like the -is verb ending). Manĝoto is someone that will be eaten etc.
You can find more about this in the grammar section of Lernu.