Voluntarul îi dă participantului numărul de concurs.

Because Romanian usually puts the definite article at the end of the noun instead of using a separate word like the.

• voluntar = a volunteer
• voluntarul = the volunteer

So Voluntarul means the volunteer.

Îi is an indirect object pronoun meaning to him / to her in many contexts, but here it refers back to participantului and marks the person who receives something.

In this sentence:

• îi dă participantului = gives to the participant

Romanian often uses this kind of doubling, where the indirect object is expressed both by:

• the pronoun: îi
• the noun phrase: participantului

This is very common and natural in Romanian.

It is not always absolutely required in every imaginable context, but in normal Romanian this doubling is very common and often preferred.

So:

• Voluntarul îi dă participantului numărul de concurs. = very natural
• Voluntarul dă participantului numărul de concurs. = possible, but less idiomatic in many contexts

For English speakers, it can feel redundant, but in Romanian it often sounds more natural.

Because participantului is in the dative case, used here for the recipient of the action.

Compare:

• participantul = the participant (subject form / nominative)
• participantului = to the participant / of the participant (dative/genitive form)

In this sentence, the participant is the one receiving the number, so Romanian uses the dative form participantului.

Dă means gives.

It comes from the verb a da = to give.

• eu dau = I give
• el/ea dă = he/she gives

The letter ă is a separate Romanian vowel, not just a decorated a. It has a short central sound, something like the a in sofa in unstressed English pronunciation.

So da and dă are different:

• da = yes
• dă = gives

For the same reason as voluntarul: Romanian adds the definite article to the end of the noun.

• număr = a number
• numărul = the number

So numărul de concurs means the competition number or the contestant number / race number, depending on context.

De concurs literally means of competition / for the competition.

In Romanian, de + noun is often used to describe the type or purpose of something. Here it tells us what kind of number it is:

• numărul de concurs = competition number
• in natural English, this could also be contest number, race number, or bib number, depending on the situation

So de concurs acts like a descriptor.

Because after de, Romanian often uses an unarticulated noun when it functions like a classifier or type description.

So:

• numărul de concurs = the competition number
• not numărul de concursul

This is similar to how English often says race number or contest number without another the inside the phrase.

The word order is:

• Voluntarul = subject
• îi dă = verb phrase with indirect object pronoun
• participantului = indirect object
• numărul de concurs = direct object

So literally it is something like:

• The volunteer gives to-the-participant the competition number

A natural English translation would be:

• The volunteer gives the participant the competition number
• or The volunteer gives the competition number to the participant

Yes, Romanian word order is more flexible than English, because case marking and pronouns help show the roles of the words.

For example, these can all be possible depending on emphasis:

• Voluntarul îi dă participantului numărul de concurs.
• Voluntarul îi dă numărul de concurs participantului.

The version you were given is very natural. Different orders can shift emphasis slightly:

• putting participantului earlier can highlight the receiver
• putting numărul de concurs earlier can highlight what is being given

Îi is pronounced as one syllable, roughly like a very quick uy or ee-like sound depending on the speaker and context.

For a learner, the important thing is:

• it is short
• it is not pronounced as two fully separate syllables
• î and i are both real Romanian vowels, so the spelling matters

You do not need to force a strong English-style pronunciation. Listening to native audio is especially helpful for forms like îi.

Yes, this specific form is masculine singular.

• participantul = the male participant
• participantului = to the male participant

For a feminine noun, the form would be different:

• participanta = the female participant
• participantei = to the female participant

So Romanian marks gender more visibly than English does.

Yes. Îi can mean to him or to her, depending on the noun or context.

So if the sentence had a feminine recipient, îi could still be used:

• Voluntarul îi dă participantei numărul de concurs.

That would mean The volunteer gives the female participant the competition number.

The dictionary forms are:

• voluntar = volunteer
• a da = to give
• participant = participant
• număr = number
• concurs = competition / contest

The sentence uses inflected forms of several of these:

• voluntarul from voluntar
• dă from a da
• participantului from participant
• numărul from număr

This is very typical of Romanian, where endings carry a lot of grammatical information.