Ayer esperé cuarenta minutos en la parada porque el metro iba con retraso.

Because they describe two different kinds of past action.

• esperé is pretérito: it presents the waiting as a completed event.
• iba is imperfecto: it gives background information or an ongoing situation.

So the idea is:

• I waited = a finished action
• the metro was running late = the situation in progress that explains why

This contrast is very common in Spanish:

• Esperé cuarenta minutos porque el metro iba con retraso.

If you changed iba to fue, it would sound unnatural here, because fue con retraso does not express the ongoing delay in the same way.

Spanish often drops subject pronouns when they are not needed, because the verb ending already shows the subject.

• esperé = I waited

So yo is unnecessary unless you want emphasis or contrast:

• Yo esperé, pero ellos se fueron.
  I waited, but they left.

In a neutral sentence, esperé by itself is perfectly normal.

Ayer means yesterday and sets the time for the whole sentence.

It does not have to be at the beginning. Spanish is flexible:

• Ayer esperé cuarenta minutos...
• Esperé ayer cuarenta minutos...
• Esperé cuarenta minutos ayer...

The first version is the most natural here because it immediately gives the time frame.

The accent mark shows both pronunciation and verb form.

• esperé = I waited
• espere = a different form, such as a formal command or present subjunctive

The accent tells you the stress falls on the last syllable:

• es-pe-RÉ

This is very important in Spanish, because accent marks can distinguish different meanings or grammatical forms.

In Spanish, expressions of duration often come directly after the verb, with no extra word.

• Esperé cuarenta minutos. = I waited forty minutes.

This is normal with time expressions:

• Dormí ocho horas.
• Estudié dos horas.

You can sometimes use durante, but here it is not necessary:

• Esperé durante cuarenta minutos.

That is grammatical, but slightly heavier and less natural in this sentence.

Because en indicates location: you were at the stop.

• en la parada = at the stop
• a la parada would suggest movement to the stop

Compare:

• Esperé en la parada. = I waited at the stop.
• Fui a la parada. = I went to the stop.

So here en is used because the sentence describes where the waiting happened.

Parada usually means stop, especially for buses and trams.
Estación means station.

With metro, many speakers would more naturally say estación:

• Esperé en la estación porque el metro iba con retraso.

So this sentence is understandable, but depending on the context, estación may sound more natural than parada for a metro.

A useful distinction is:

• parada = stop
• estación = station
• andén = platform

Because porque is the conjunction meaning because.

• porque = because
• por qué = why

Examples:

• Esperé porque el metro iba con retraso. = I waited because the metro was delayed.
• ¿Por qué esperaste? = Why did you wait?

This is one of the most common spelling distinctions in Spanish.

Iba con retraso is a very natural way to say that a train, bus, flight, etc. was running late or delayed.

Literally, it is something like:

• was going with delay

It does not sound natural word-for-word in English, but in Spanish it is standard.

Estaba retrasado can sometimes be understood, but for transport, ir con retraso is often more idiomatic in everyday use.

Very common alternatives:

• El metro iba con retraso.
• El metro llevaba retraso.
• El metro estaba retrasado.
  This is understandable, but often a little less idiomatic.

Not in exactly the same way.

• iba con retraso means the service itself was delayed
• llegaba tarde means it was arriving late

Both can work in some contexts, but they focus on slightly different things:

• El metro iba con retraso. = The metro was running late.
• El metro llegaba tarde. = The metro was arriving late.

In your sentence, iba con retraso is broader and very natural for general disruption or delay.

Yes, the order can change.

The original order is very natural:

• Ayer esperé cuarenta minutos en la parada porque el metro iba con retraso.

But you can also put the reason first:

• Porque el metro iba con retraso, ayer esperé cuarenta minutos en la parada.

That is grammatical, but it sounds more marked or emphatic. In everyday speech, Spanish usually gives the main action first and the reason after it.

A very natural version in Spain might be:

• Ayer esperé cuarenta minutos en la estación porque el metro iba con retraso.

Or even:

• Ayer tuve que esperar cuarenta minutos porque el metro iba con retraso.

Why?

• estación often sounds more natural than parada with metro
• tuve que esperar adds the idea of I ended up having to wait

But the original sentence is still useful for learning common grammar:

• pretérito + imperfecto
• dropped subject pronoun
• duration with no preposition
• ir con retraso for transport delays