На табло видно, что наш рейс вылетает через час.

На табло means on the display / on the board.

• на often means on
• табло means a display board, such as an airport departures board

After на with the meaning of location, Russian normally uses the prepositional case.
However, табло is one of those nouns that is usually indeclinable, so its form does not change:

• nominative: табло
• prepositional: на табло

So even though it is functioning like a prepositional form, it still looks exactly the same.

Here видно is an impersonal predicate, meaning something like:

• it is visible
• one can see
• it can be seen

So На табло видно, что... literally means something like:

• On the board, it is visible that...

Russian often uses impersonal constructions where English would prefer something more personal, like We can see on the board that... or simply The board shows that...

There is no subject because видно here does not need one.

Because что introduces a subordinate clause:

• На табло видно, что наш рейс вылетает через час.

The first part is the main clause:

• На табло видно = It is visible on the board

The second part explains what is visible:

• что наш рейс вылетает через час = that our flight leaves in an hour

In Russian, a comma is normally required before что when it means that and introduces a clause.

Наш рейс is the subject of the subordinate clause:

• наш рейс вылетает через час
• our flight departs in an hour

Since it is the subject, it is in the nominative case:

• наш = our
• рейс = flight

So:

• nominative: наш рейс
• genitive: нашего рейса
• accusative: often наш рейс for an inanimate noun, but not the role here

This is very common in Russian.

Вылетает is grammatically present tense, but it is often used for scheduled future events, just like English can say:

• Our flight leaves in an hour
• The train arrives at 8
• The meeting starts tomorrow

So вылетает через час means:

• departs in an hour
• not is departing right now

Russian uses the present tense of an imperfective verb very naturally for timetables, schedules, and planned events.

Yes, you could, but the nuance changes a little.

• вылетает через час = the flight is scheduled to leave in an hour; this sounds very natural for timetables and travel information
• вылетит через час = the flight will leave in an hour; this focuses more on the future result/event itself

At an airport board, вылетает sounds especially natural because it fits the idea of a scheduled departure.

Good question. They are related but not the same.

• лететь / летит = to fly / is flying
• вылетать / вылетает = to depart by air / takes off / leaves

So:

• Самолёт летит = The plane is flying
• Рейс вылетает в 10:00 = The flight departs at 10:00

In airport language, вылетать is the normal verb for a flight leaving.

Через does often mean through, but it also has a time meaning:

• через час = in an hour
• через минуту = in a minute
• через два дня = in two days

So Russian uses через + time expression for something happening after that amount of time.

This is a very common pattern.

After через in this time meaning, Russian uses the accusative case.

So:

• час is the accusative singular here
• через час = in an hour

More examples:

• через минуту = in a minute
• через день = in a day
• через неделю = in a week

With some nouns, the accusative looks the same as the nominative, especially for inanimate nouns. In час, the form also happens to be час.

Yes. Russian word order is flexible, though different orders can shift emphasis.

The given sentence:

• На табло видно, что наш рейс вылетает через час.

This sounds natural and starts with the source of information: on the board.

You could also hear:

• Видно на табло, что наш рейс вылетает через час.
• Что наш рейс вылетает через час, видно на табло.

These are grammatically possible, but the original version is probably the most neutral and natural in this context.

Yes, табло is a normal and common word for a display board or information board, including at airports and stations.

Depending on context, Russian might also use more specific expressions such as:

• информационное табло = information board
• табло вылетов = departures board

But in your sentence, simply на табло sounds completely natural.

It is mostly neutral and very natural.

It would fit:

• everyday conversation
• travel situations
• written or spoken standard Russian

It is not especially formal, and it is not slangy either.

A very conversational English translation might be:

• The board shows our flight leaves in an hour.

But the Russian itself is standard and broadly usable.