Il manometro mostra la pressione di estrazione.

Il is the masculine singular definite article, equivalent to the.

So il manometro means the pressure gauge.
Italian nouns normally need an article much more often than English nouns do, especially in full sentences.

Also, manometro is a masculine singular noun, so il is the correct article.

Because pressione is a feminine singular noun, so it takes la.

A useful pattern: many Italian nouns ending in -zione or -sione are feminine, such as:

• la pressione
• la situazione
• la decisione

So la pressione is grammatically the correct form.

Mostra is the third-person singular present tense of mostrare = to show.

The subject is il manometro, which is singular, so the verb must also be singular:

• io mostro = I show
• tu mostri = you show
• lui/lei mostra = he/she/it shows

So Il manometro mostra... = The gauge shows...

Italian usually does not need an explicit subject pronoun when the subject is already clear.

In this sentence, the subject is already stated as il manometro, so there is no need to add a pronoun.

This is very normal in Italian. In fact, adding a pronoun here would usually sound unnecessary.

Because mostrare normally takes a direct object.

You show something:

• mostrare un valore
• mostrare la temperatura
• mostrare la pressione

So la pressione di estrazione is simply the direct object of mostra. No extra preposition is needed.

Here di links two nouns together.

Literally, it is something like pressure of extraction, but in natural English we usually say extraction pressure.

This noun + di + noun structure is extremely common in Italian, especially in technical language:

• temperatura di esercizio = operating temperature
• tempo di attesa = waiting time
• pressione di estrazione = extraction pressure

So di is functioning like a connector where English often uses another noun as an adjective-like modifier.

Because estrazione is being used in a general, classifying way.

Pressione di estrazione means the kind of pressure related to extraction. It names a category or function.

If you said dell'estrazione, that would sound more like of the extraction, referring to a specific extraction already identified in the conversation.

So:

• pressione di estrazione = extraction pressure, extraction-related pressure
• pressione dell'estrazione = the pressure of the extraction, referring to a specific extraction

In a technical sentence like this, di estrazione is the natural choice.

Yes.

The Italian present tense often covers both:

• shows
• is showing

So Il manometro mostra la pressione di estrazione can mean:

• the gauge shows the extraction pressure
• the gauge is showing the extraction pressure

The exact English choice depends on context.

Yes. This is the most neutral and standard order:

subject + verb + object

• Il manometro = subject
• mostra = verb
• la pressione di estrazione = object

Italian can change word order for emphasis, but in a normal technical statement this version is the most natural.

In a full sentence, usually no. Italian generally keeps the articles:

• Il manometro mostra la pressione di estrazione.

However, in a label, heading, or note, articles are more likely to be dropped:

• Manometro
• Pressione di estrazione
• Valore massimo

So article omission is possible in technical formatting, but not usually in a normal sentence like this one.

The main changes would be:

• il manometro → i manometri
• mostra → mostrano
• la pressione → le pressioni if that noun is also plural

For example:

• I manometri mostrano la pressione di estrazione.
  = The gauges show the extraction pressure.

Or, if both nouns are plural:

• I manometri mostrano le pressioni di estrazione.

This is a useful pattern to notice:

• singular -o often becomes plural -i
• singular verbs change too: mostra → mostrano