Perdón por llegar tarde; había mucho tráfico.

Both can be used to apologize, but they are not exactly the same.

• Perdón is very common for a direct apology, especially for something practical or immediate.
• Lo siento can sound a bit more emotional or heartfelt.

In Perdón por llegar tarde, the speaker is simply apologizing for being late, so Perdón sounds very natural.

You could also say:

• Perdón por llegar tarde.
• Lo siento por llegar tarde.

Both are correct, but Perdón is especially common in everyday speech.

After perdón, Spanish often uses por to mean for when giving the reason for the apology.

So:

• Perdón por llegar tarde = Sorry for arriving late / Sorry for being late

This pattern is very common:

• Perdón por interrumpir. = Sorry for interrupting.
• Gracias por venir. = Thanks for coming.

So por + infinitive is a very useful structure to learn.

In Spanish, to be late is usually expressed with llegar tarde, literally to arrive late.

So:

• llegar tarde = to arrive late / to be late

Examples:

• Siempre llego tarde. = I’m always late.
• Llegaste tarde otra vez. = You were late again.

Spanish does not normally say ser tarde for a person being late.
Es tarde means It’s late, talking about the time, not about a person.

Había is the imperfect form of haber, and it is used here to describe background circumstances.

• Había mucho tráfico = There was a lot of traffic

The imperfect fits well because the traffic is presented as an ongoing situation in the background, explaining why the person was late.

Compare:

• Había mucho tráfico. = There was a lot of traffic.
  (background situation, description)
• Hubo un accidente. = There was an accident.
  (a specific event that happened)

In this sentence, Spanish prefers había mucho tráfico because it gives the context or excuse.

Había comes from haber, and in this use it means there was / there were.

So:

• había tráfico = there was traffic
• había mucha gente = there were a lot of people

This is an impersonal use, so it does not have a normal subject like English there.
Spanish simply uses haber by itself.

Very useful pattern:

• Hay = there is / there are
• Había = there was / there were
• Habrá = there will be

Because tráfico is a singular noun.

In Spanish, tráfico usually works like an uncountable noun here, similar to traffic in English. So you say:

• mucho tráfico = a lot of traffic

Not:

• muchos tráfico

The adjective/quantifier must agree with the noun:

• mucho tráfico
• mucha gente
• muchos coches
• muchas personas

Yes. Both are correct.

• Había tráfico = There was traffic
• Había mucho tráfico = There was a lot of traffic

Adding mucho makes the excuse stronger and more specific. It suggests the traffic was especially bad.

Spanish often drops subject pronouns when they are not needed, because the verb forms usually make the subject clear or because the context already does.

In this sentence:

• Perdón por llegar tarde
• había mucho tráfico

There is no need to say yo. A Spanish speaker understands that the person apologizing is talking about their own lateness.

If you said Yo llegué tarde, the yo would usually add emphasis or contrast.

The semicolon connects two closely related parts:

• Perdón por llegar tarde
• había mucho tráfico

It shows that the second part explains the first one. In English, this is similar to writing:

• Sorry for being late; there was a lot of traffic.

In everyday Spanish, many people would also use:

• a full stop: Perdón por llegar tarde. Había mucho tráfico.
• a comma: Perdón por llegar tarde, había mucho tráfico.

The semicolon is just a slightly more formal or careful punctuation choice.

No, that would not sound natural.

To say to be late, Spanish normally uses:

• llegar tarde

So the correct phrase is:

• Perdón por llegar tarde

Estar tarde is not the normal way to express a person being late.

Yes, depending on the situation.

• Perdón = sorry / excuse me
• Disculpa = informal singular (you = tú)
• Disculpe = formal singular (you = usted)

Examples:

• Perdón por llegar tarde.
• Disculpa por llegar tarde.
• Disculpe por llegar tarde.

These are all possible, but Perdón is very neutral and common.

In Spain, había is pronounced roughly like ah-BEE-ah.

A few helpful points:

• The h is silent.
• The stress is on bí.
• The written accent in había shows where the stress goes.

So it is not pronounced like HA-bia. The first sound is just the vowel sound: a.

Yes, very natural.

A speaker in Spain would easily say:

• Perdón por llegar tarde; había mucho tráfico.

It sounds normal and idiomatic. In more casual conversation, someone might also say:

• Perdón por el retraso; había mucho tráfico.
• Lo siento, llego tarde por el tráfico.
• Perdona el retraso, había mucho tráfico.

But the original sentence is absolutely natural in Spanish from Spain.