densya no tien no tame, kaigi ni sukosi okuremasita.

They are doing two separate linking jobs.

• 電車の遅延 = the train’s delay / train delay
  • Here, の connects 電車 and 遅延.
• 電車の遅延のため = because of the train delay
  • Here, the second の connects the whole noun phrase 電車の遅延 to ため.

A good way to see it is:

• 電車 = train
• 遅延 = delay
• ため = because of / due to

So the structure is basically:

[train delay] + because of

In this sentence, ため means because of or due to.

So:

• 電車の遅延のため = due to the train delay

This use of ため is a bit more formal and written-sounding than casual から or ので.

For example:

• 電車が遅れたので、会議に遅れました。 = Because the train was delayed, I was late to the meeting.

That is more conversational.
Your original sentence sounds natural and slightly more formal, like something you might say in a workplace or write in a message.

遅延 is a noun meaning delay.
So 電車の遅延 is a noun phrase: train delay.

Japanese often expresses reasons in a compact, formal way by using nouns like this.

Compare:

• 電車の遅延のため
  = due to the train delay

  • more formal, compact

• 電車が遅れたため
  = because the train was delayed

  • same basic meaning, but using a verb clause

Both are correct. The version with 遅延 sounds especially common in announcements, business contexts, and formal explanations.

The verb 遅れる normally uses に for the event, place, or time that someone is late for.

So:

• 会議に遅れる = to be late for a meeting
• 学校に遅れる = to be late for school
• 約束に遅れる = to be late for an appointment

Using を here would not be natural.

A helpful way to think of に here is: it marks the target or point you failed to arrive at on time.

Because 遅れる means to be late, and that is exactly what happened.

• 会議に遅れました = I was late to the meeting

Other verbs would change the meaning:

• 会議に行きませんでした = I did not go to the meeting
• 会議に間に合いませんでした = I did not make it in time for the meeting

So 遅れました implies the speaker did go, but arrived late.

少し means a little or slightly.

In this sentence, it modifies 遅れました:

• 少し遅れました = I was a little late

It tells you the lateness was not severe.

You could also hear:

• ちょっと遅れました = a little late
  
  • more casual
• 少々遅れました = slightly late
  
  • more formal

So 少し is a neutral and natural choice.

The subject is omitted, which is very common in Japanese.

From context, 遅れました strongly suggests something like:

• 私は会議に少し遅れました。 = I was a little late to the meeting.

Japanese often leaves out subjects when they are obvious from the situation.

So even though 私 is not written, the sentence naturally means that the speaker was late.

It can often be understood more broadly as the train or train service, depending on context.

In Japanese, 電車の遅延 does not always force a strict distinction between:

• a specific train being delayed
• the train system / line experiencing delays

In real life, this phrase often means there was a delay with the train I was taking or train delays occurred.

So the exact English translation can vary a little:

• because of a train delay
• because the train was delayed
• due to train delays

Yes, absolutely. That is a very natural alternative.

Compare the two:

• 電車の遅延のため、会議に少し遅れました。

  • more noun-based
  • slightly more formal or official

• 電車が遅れたため、会議に少し遅れました。

  • more verb-based
  • also natural
  • feels a little more direct

Both mean essentially the same thing.

Yes, it is polite and somewhat formal.

Reasons:

• 遅延 is a formal-style noun
• ため sounds more formal than casual から
• 遅れました uses polite ます form

So this sentence fits well in situations like:

• explaining yourself at work
• sending a polite message
• speaking to a superior
• making a formal excuse

A more casual version might be:

• 電車が遅れたので、会議にちょっと遅れました。

That means the same thing, but sounds more conversational.

The comma helps separate the reason from the main statement.

So the sentence is divided into:

• 電車の遅延のため、 = because of the train delay,
• 会議に少し遅れました。 = I was a little late to the meeting.

The comma is very natural here because the reason comes first and is a bit long. It makes the sentence easier to read.

You may sometimes see similar sentences without a comma, but using one here is standard and clear.