Questions & Answers about Teskeiðin datt af borðinu.
They are:
So the sentence is built from very common Icelandic pieces: a noun, a past-tense verb, a preposition, and another noun.
Because Icelandic usually puts the definite article onto the end of the noun instead of using a separate word like English the.
- teskeið = teaspoon
- teskeiðin = the teaspoon
Here, the ending -in is the definite article attached to a feminine singular noun in the nominative.
Teskeiðin is nominative singular because it is the subject of the sentence — it is the thing doing the falling.
A good way to see that is to ask: What fell off the table?
Answer: The teaspoon.
That makes teskeiðin the subject, so nominative is the expected case.