How can you use the imperative in the third person?
I only took up Italian yesterday, so I'm a complete beginner. There's something in my textbook that's got me confused.

It's in a section talking about using an imperative. The book has a table of verb endings there. The thing that's got me confused is that it lists imperative endings for verbs in the third person. I'm baffled because I can't imagine how it's logically possible to use an imperative in anything other than the second person. I tried to find a solution using Google and found that the 1st person plural imperative is equivalent to saying "Let's..." in English, but I'm still confused about the third person imperative. I thought at first that the 3rd person singular conjugation must only be used for plural "you" (which uses 3rd person singular conjugation), but that doesn't explain the 3rd person plural form.

My best guess it that it's similar to "He'd better...", but that doesn't seem the same as an imperative to me. Could someone please explain this to me?I reached the character limit so I couldn't add any more details. As a random example the book says a verb ending with '-are' takes an '-a' ending with 'tu', '-i' with 'lui/lei/Lei', '-iamo' with 'noi', '-ate' with 'voi', and '-ino' with 'loro'.

Question

How can you use the imperative in the third person?
I only took up Italian yesterday, so I'm a complete beginner. There's something in my textbook that's got me confused.

It's in a section talking about using an imperative. The book has a table of verb endings there. The thing that's got me confused is that it lists imperative endings for verbs in the third person. I'm baffled because I can't imagine how it's logically possible to use an imperative in anything other than the second person. I tried to find a solution using Google and found that the 1st person plural imperative is equivalent to saying "Let's..." in English, but I'm still confused about the third person imperative. I thought at first that the 3rd person singular conjugation must only be used for plural "you" (which uses 3rd person singular conjugation), but that doesn't explain the 3rd person plural form.

My best guess it that it's similar to "He'd better...", but that doesn't seem the same as an imperative to me. Could someone please explain this to me?I reached the character limit so I couldn't add any more details. As a random example the book says a verb ending with '-are' takes an '-a' ending with 'tu', '-i' with 'lui/lei/Lei', '-iamo' with 'noi', '-ate' with 'voi', and '-ino' with 'loro'.

Answer

It's probably a formal imperative. In Italian, what is nominally the third person singular or plural is used to show politeness or respect, so Lei or (less commonly, at least that's my impression) Loro instead of tu or voi.  For this imperative, the subjunctive mood is also used  (venga/vengano nstead of vieni/venite).

Answer

English doesn't really have an equivalent of the third person imperative, but it can often be roughly translated by phrases such as: Let him/her/it..., May he/she/it..., He/she/it can...

Some examples:
Chi vuole torta, si tagli una fetta (Whoever wants cake, let him cut himself a slice)
Che piova pure, tanto l'ombrello ce l'ho (Let it rain, I've got my umbrella)
I politici? che vadano al diavolo (Politicians can go to hell)
Viva il re (long live the king - "viva" is actually a fossilised form and so it can also be used in the plural, but it was originally the 3rd person singular imperative of "vivere" - "to live")

By the way, the 3rd person imperative is nothing more than the present subjunctive of the verb, if that's any help to you.

Answer

Pay attention! 
What Coligno said is right but they aren't imperative forms, they are simply subjunctives. 
As Bergmann said, Italian language use the singular and plural third persons as a formal (polite) way to address respectively the singular and plural second persons singular. This is the aim of the imperative forms on the third persons, to give orders to person, with which you aren't on a first-name basis. 
informal second person singular: "Mario, vieni qui!" (... come here!) 
formal second person singular: "Signor Rossi, venga qui!" 
informal second person plural: "Mario e Anna, venite qui!" 
formal second person plural: "Signori Rossi, vengano qui!" 
Anyhow, the imperative forms on the third persons are made with the present tense of the subjunctive mood. 
By the way, there is a imperative form also for the first plural person, corresponding to the English construction "let's", it is the the present tense of indicative or subjunctive mood (they are even identical): "andiamo!" (let's go!) 
I have spoken about "imperative forms" because the "imperative mood", also in Italian, are only on the second persons.