La instruistino klarigis la regulon simple, por ke ĉiu studento komprenu ĝin.

Esperanto words are often built from clear pieces:

• instru- = teach
• -ist- = a person who does something as an occupation or regular activity
• -in- = female
• -o = noun ending

So:

• instruisto = teacher
• instruistino = female teacher

This kind of word-building is very common in Esperanto.

klarigis comes from klarigi, which means to make clear or to explain.

It breaks down like this:

• klar- = clear
• -ig- = make something become / cause to be
• -i = infinitive ending

So klarigi literally means to make clear.

Then -is marks the past tense:

• klarigas = explains
• klarigis = explained
• klarigos = will explain

The -n shows the direct object.

In this sentence, the teacher explained the rule, so the rule is what received the action. That is why it is:

• la regulo = the rule
• la regulon = the rule, as a direct object

This accusative -n is one of the most important parts of Esperanto grammar.

Because simple is an adverb, not an adjective.

• simpla = simple
• simple = simply

Here it describes how she explained the rule, so an adverb is needed:

• klarigis ... simple = explained ... simply

If you used simpla, it would describe a noun instead.

por ke means so that or in order that.

It introduces a purpose clause:

• La instruistino klarigis la regulon simple = The teacher explained the rule simply
• por ke ĉiu studento komprenu ĝin = so that every student would understand it

So the second part gives the purpose of the first part.

After por ke, Esperanto normally uses the -u verb form.

So:

• komprenas = understands / is understanding
• komprenu = understand, in the -u form

In this kind of sentence, -u does not mean a command. It is the normal form after por ke to express purpose:

• por ke ... komprenu = so that ... may understand / would understand

English speakers sometimes compare this loosely to a subjunctive idea, but in Esperanto it is simply the standard pattern: por ke + -u.

Because ĉiu means each or every individual one, and it normally goes with a singular noun:

• ĉiu studento = each student / every student

If you say ĉiuj studentoj, that means all the students as a group.

So there is a small difference:

• ĉiu studento = every student, one by one
• ĉiuj studentoj = all students, taken together

Both can often translate naturally into English, but the Esperanto grammar is different.

ĝin refers back to la regulon.

• ĝi = it
• ĝin = it, as a direct object

In the clause ĉiu studento komprenu ĝin, the students understand it, and it means the rule.

The -n is there again because ĝin is the direct object of komprenu.

la is the definite article, meaning the.

So:

• la instruistino = the teacher
• la regulon = the rule

Esperanto has only one definite article: la. It never changes form.

Also, Esperanto has no indefinite article. So:

• instruistino can mean a teacher or just teacher, depending on context
• la instruistino means the teacher

Not as strictly as in English.

Because Esperanto marks the direct object with -n, word order can be more flexible. This sentence uses a very normal and clear order:

• La instruistino = subject
• klarigis = verb
• la regulon = object
• simple = adverb
• por ke... = purpose clause

You could move some parts for emphasis, but this version is the most straightforward for learners.

Yes. Adverbs in Esperanto can often move around more freely than in English.

For example, these are all understandable:

• La instruistino simple klarigis la regulon...
• La instruistino klarigis simple la regulon...
• La instruistino klarigis la regulon simple...

The version in your sentence is very natural. Placing simple after la regulon clearly shows that it modifies klarigis.

The special letters here are:

• ĉ = like ch in church
• ĝ = like j in judge

So approximately:

• ĉiu ≈ CHEE-oo
• ĝin ≈ JEEN

A few extra notes:

• Esperanto stress is usually on the second-to-last syllable
• So ĉiu is stressed on ĉi
• ĝin is only one syllable

These pronunciation rules are very regular in Esperanto.