De dertiende afspraak is morgen.

Because afspraak is a de-word in Dutch: de afspraak.

Dutch singular nouns are either de words or het words, and you usually have to learn that with each noun. There is no reliable way to guess it from the English meaning alone.

A few useful forms:

• de afspraak = the appointment
• een afspraak = an appointment
• de afspraken = the appointments

Dertiende is the ordinal form of dertien.

So:

• dertien = thirteen
• dertiende = thirteenth

Dutch ordinal numbers work much like English ones:

• eerste = first
• tweede = second
• derde = third
• vierde = fourth
• dertiende = thirteenth

In this sentence, dertiende describes afspraak, so it means the thirteenth appointment.

Because morgen here is being used as an adverb meaning tomorrow.

Dutch time words like these usually do not need an article or preposition:

• vandaag = today
• morgen = tomorrow
• gisteren = yesterday

So:

• De afspraak is morgen. = The appointment is tomorrow.

You do not say op morgen in this meaning.

Here it means tomorrow.

That is clear because it comes after is and tells you when the appointment is.

Dutch morgen can also be related to morning, but in modern everyday Dutch, if you specifically mean in the morning, people more often say:

• 's morgens
• morgenochtend
• in de ochtend

So in this sentence, the natural reading is definitely tomorrow.

Because this is a normal Dutch main clause, and Dutch main clauses follow the verb-second rule.

Here the structure is:

• De dertiende afspraak = subject
• is = verb
• morgen = time expression

So the finite verb is comes in the second main position:

• De dertiende afspraak is morgen.

This is very typical Dutch word order.

Yes, that is grammatical.

Dutch often allows you to move another element to the first position for emphasis or topic, but the verb still stays second:

• De dertiende afspraak is morgen.
• Morgen is de dertiende afspraak.

The second version puts more focus on morgen. It can sound natural if you are answering a question like When is the thirteenth appointment?

In this sentence, afspraak most naturally means appointment.

But afspraak is a flexible word in Dutch. Depending on context, it can also mean:

• an arranged meeting
• an appointment
• an agreement
• an arrangement

For example:

• Ik heb een afspraak met de tandarts. = I have a dentist appointment.
• Dat was niet de afspraak. = That was not the agreement.

So the exact nuance depends on context, but appointment is the most likely meaning here.

By default, it most naturally means the thirteenth appointment in a sequence.

If you want to say the appointment on the 13th, Dutch would usually make that clearer, for example with:

• de afspraak op de dertiende
• de afspraak op 13 maart
• de afspraak op de dertiende van de maand

So without extra context, de dertiende afspraak is normally understood as appointment number thirteen, not the appointment scheduled for the 13th day of the month.

A rough English-friendly approximation is:

• dertiende ≈ der-TEEN-duh
• afspraak ≈ AHF-spraak

A few pronunciation notes:

• In dertiende, the stress is on -tien-
• The final -e in dertiende is a weak sound like the a in sofa
• In afspraak, aa is a long vowel
• The r and vowels are still Dutch sounds, so the English approximation is only approximate

Because Dutch does not capitalize ordinary words like English sometimes does in special contexts.

So:

• morgen is lowercase
• dertiende is lowercase
• afspraak is lowercase

You only capitalize them if they start the sentence or are part of a proper name.