Hier, c'est le jour qui précède aujourd'hui.

Because Hier is being presented as the topic, almost like a heading: Yesterday — it is the day that comes before today.

This is common in definitions and explanations. The comma shows that Hier is detached from the rest of the sentence and is the thing being defined.

So this structure is a bit like:

Hier, c'est... = As for yesterday, it is...

French normally uses c'est when identifying or defining something with a noun phrase.

Here, le jour qui précède aujourd'hui is a noun phrase, so c'est is the natural choice.

• C'est le jour... = correct
• Il est le jour... = not natural here

A useful rule is:

• c'est
  • noun = very common
• il est
  • adjective = very common

For example:

• C'est un problème.
• Il est important.

In your sentence, French is defining what hier is, so c'est fits perfectly.

Because French usually needs an article before a singular countable noun in this kind of sentence.

So French says:

• le jour = the day

Using jour by itself here would sound incomplete. English can sometimes leave articles out more easily than French, but French usually cannot.

Here, qui means that or which and introduces a relative clause:

• le jour = the day
• qui précède aujourd'hui = that comes before today

So qui connects le jour to extra information about that day.

A literal breakdown is:

• le jour = the day
• qui = that
• précède = precedes / comes before
• aujourd'hui = today

Because qui is the subject of the verb précède.

In this clause, le jour is the thing doing the action of preceding:

• Le jour précède aujourd'hui.

Since the relative pronoun stands for the subject, French uses qui.

Very roughly:

• qui = the one that does the action
• que = the one that receives the action

So here:

• le jour qui précède aujourd'hui = the day that precedes today

Because the sentence needs a conjugated verb, not an infinitive.

The base form is précéder = to precede

But after qui, French needs a finite verb that agrees with le jour, which is third person singular. So:

• il précède
• le jour qui précède aujourd'hui

So précède is the present-tense form of précéder for he/it.

Because this is a definition, not a past event.

The sentence is saying something generally true about the word hier. French often uses the present tense for definitions, facts, and general truths.

It is similar to English sentences like:

• A triangle has three sides.
• Winter comes after autumn.

Even though yesterday refers to the past, the definition itself is true at the present moment, so French uses the present: précède.

Because précéder takes a direct object in French.

So French says:

• précéder quelque chose = to precede something

That is why you get:

• qui précède aujourd'hui

and not something like qui précède à aujourd'hui.

English works similarly with precede:

• the day that precedes today

It is grammatical and correct, but it sounds like a definition, an explanation, or something from a lesson or dictionary.

In normal conversation, people would not usually define hier this way unless they were teaching or clarifying language.

So the sentence is natural in a teaching or explanatory context, but not something you would hear often in everyday casual speech.

A careful pronunciation in standard French is approximately:

/jɛʁ sɛ lə ʒuʁ ki pʁe.sɛd o.ʒuʁ.dɥi/

A rough English-friendly guide would be:

yair, say luh zhoor kee pray-said oh-zhoor-dwee

A few helpful points:

• Hier is usually one syllable
• c'est sounds like say
• jour has the French j sound, like the s in measure
• précède has an open è sound in the last syllable
• aujourd'hui is pronounced as one word, with the last part sounding like dwee

Not perfectly. A very literal translation would be:

Yesterday, it is the day that precedes today.

That is understandable in English, but it sounds stiff. English would more naturally say:

Yesterday is the day before today.

So the French structure is fine, but if you copy it word for word into English, the result may sound more formal or awkward than normal English.