الرقصة الأولى بين المأدبة والتهنئة في برنامج الحفل.

Because رقصة is a feminine noun, so the ordinal adjective first must also be feminine.

• رقصة = dance
• الأولى = first (feminine form)

In Arabic, adjectives agree with the noun they describe in:

• gender
• definiteness
• number

So:

• الرقصة الأولى = the first dance

If the noun were masculine, you would use الأول instead:

• الكتاب الأول = the first book

Because in Arabic, adjectives normally come after the noun they describe.

So:

• الرقصة الأولى
  literally: the dance the-first
  natural English: the first dance

This is the normal Arabic pattern:

• البيت الكبير = the big house
• الفتاة الجميلة = the beautiful girl

Because Arabic adjectives must match the noun in definiteness as well.

Here, الرقصة is definite because it has الـ:

• الرقصة = the dance

So the adjective must also be definite:

• الأولى = the first

That gives:

• الرقصة الأولى = the first dance

Compare:

• رقصة أولى = a first dance
• الرقصة الأولى = the first dance

Yes.
الأول is the masculine form, and الأولى is the feminine form.

Examples:

• اليوم الأول = the first day (masculine noun)
• الرقصة الأولى = the first dance (feminine noun)

This pair is somewhat irregular compared with many other adjectives, so it is worth memorizing:

• masculine: أول / الأول
• feminine: أولى / الأولى

بين means between.

In this sentence, it shows where the first dance falls within the schedule:

• بين المأدبة والتهنئة
  = between the banquet and the congratulatory segment / felicitations

So the idea is not physical location, but position in the program.

Because بين usually connects two things:

• بين X و Y = between X and Y

Here:

• المأدبة = the banquet
• التهنئة = the congratulation / felicitations / congratulatory part

So:

• بين المأدبة والتهنئة = between the banquet and the felicitations

This is a very common structure in Arabic.

المأدبة means banquet, feast, or formal meal.

It often suggests a more formal or special meal than just ordinary food. In the context of a celebration or wedding program, المأدبة would likely mean the meal or banquet portion of the event.

التهنئة literally means congratulation or offering congratulations.

In this kind of event context, it may refer to:

• a congratulatory segment
• people coming to congratulate the hosts or couple
• formal greetings or well-wishes

So in natural English, you might understand it as something like:

• the felicitations
• the congratulations segment
• the greeting/congratulatory part of the program

Because Arabic often allows verbless sentences, especially in:

• titles
• captions
• schedules
• headings
• program notes

This sentence sounds like the kind of thing you might see in an event program, where full sentences are not always necessary.

So instead of saying something fully explicit like:

• الرقصة الأولى تكون بين المأدبة والتهنئة في برنامج الحفل = The first dance is between the banquet and the felicitations in the program

Arabic can simply say:

• الرقصة الأولى بين المأدبة والتهنئة في برنامج الحفل

This is shorter and very natural in a schedule-style context.

في means in.

So:

• في برنامج الحفل = in the event program / in the ceremony program

This phrase tells you the context in which the ordering is being described. It means the first dance comes between those two parts in the schedule of the event.

Because برنامج الحفل is an iḍāfa construction, which is very common in Arabic.

An iḍāfa links two nouns, often like English X of Y or sometimes just Y X:

• برنامج الحفل = the program of the ceremony/event
• more naturally: the event program

So:

• برنامج = program
• الحفل = the celebration / ceremony / party

This is more natural in Arabic than using لـ here.

الحفل can mean several related things depending on context:

• party
• celebration
• ceremony
• event

In a formal context like this one, event or ceremony may sound best. If the sentence is about a wedding, it could also be understood as the wedding celebration.

So برنامج الحفل could be translated as:

• the event program
• the ceremony program
• the program of the celebration

Most likely schedule order.

Even though بين literally means between, here the phrase:

• بين المأدبة والتهنئة في برنامج الحفل

strongly suggests:

• the first dance takes place between the banquet and the congratulatory segment in the program

So it is probably about when the dance happens, not where it happens.

Yes. A more natural English rendering would usually be something like:

• The first dance comes between the banquet and the felicitations in the event program.
• In the event program, the first dance is scheduled between the banquet and the congratulatory segment.

A word-for-word translation can sound awkward in English, so it is normal to smooth it out.