In my textbook the word надо is translated into: "It is needed" and нужен: "needed". As russian speaker. When do you use these two words, are there any nuances?
надо is more colloquial than
To say [somebody] needs [something] you use the two words in such a way: [somebody in the Dat. case] надо/нужен [something in the Nom. case]. Note,
надо never changes its form, but
нужен must agree in number and gender with the subject of the sentence, that is the part which is in the Nominative case. For example:
I need a pencil.
Мне надо карандаш.
Мне нужен карандаш.
Oleg needs a pen.
Олегу надо ручка.
Олегу нужна ручка.
Still, in sentences like [somebody] needs [something],
нужен is used more often.
There is another way to use the two words, it is when you want to say [somebody] needs [to do something]. In this case,
нужен is used in the neuter gender,
нужно, and both words are absolutely interchangeable. The construction is like this: [somebody in the Dat. case] надо/нужно [infinitive phrase]. For example:
I need to go.
Мне надо/нужно уходить.
You need to see that.
Вам надо/нужно это увидеть.
Нужный is an adjective meaning "needed", "required", "necessary".
Нужен / Нужна is a short adjective made of the full form нужный. Short adjectives often are the part of predicative (e.g. "Я им нужен") but they are still adjectives.
Нужно / Надо are purely impersonate constructions like, say, Spanish hay que. The closest English equivalent would be "It is needed". The difference between надо and нужно is very, very slight. You may simply ignore it for a moment.
P.S. Technically, нужно is the neuter gender of the short adjective нужен / нужна but in the vast majority of cases нужно stands for an impersonate, not for an adjective.