The following (starting with 'Tips and notes) is taken from the first lesson on adjectives from the lesson notes to the Duolingo Danish lessons. If you use the app they may not be easy to find, but on the Duolingo.com site they accompany each lesson as you progress. I am sort of wondering how you got all the way to level 17 without reading this ... ;-)
The 'er' is merely the simple present form of at være, to be.
En gård, gården, det er en stor gård, den store gård, de store gårde
A farm, the farm, it is a big farm, the big farm, the big farms
Et hus, huset, det er et stort hus, det store hus, de store huse
A house, the house, it is a big house, the big house, the big houses
The question is not why is there a -t at the end of the adjective describing a noun in the neuter gender, the question is why you would believe it should not be there! But this might help you a little:
Tips and notes
Since we have already introduced how to work adjectives in the Colors skill, let us just quickly recap what we learned earlier.
Adjectives decline according to the gender and number of the noun that they modify. In Danish you would say a big apple with the sentence et stort æble. You have already seen et æble, so let us discuss the middle part: stort. Stor is the Danish word for big (along with several other words). When used to describe a neuter gender noun such as æblet it is then suffixed by -t and becomes stort.
There are three ways an adjective can be declined: -, -t, or -e. - is used for common gender nouns, -t is used for neuter gender nouns, and -e is used for plural. This is also described in the following table:
Common Neuter Singular - -t Plural -e -e There are irregular adjectives that are missing one or more of the forms, such as beskidt (dirty), which can only be beskidt or beskidte. Here beskidt is used for both of the singular forms: En beskidt abe (a dirty monkey). Other words, such as moderne (modern) are irregular in a different way and only have one form used for all nouns: et moderne bord (a modern table).
Adjectives and Definite Nouns
While nouns normally express definiteness using a postfix, this changes to using an article if any adjectives is attached to the noun.
If the adjective is used with a definite noun, then it is put between the definite article and the noun: En åben bil (an open car) becomes den åbne bil (the open car). In this case the adjective is declined the same way as for the plural, no matter the grammatical number or gender of the noun.
As a reminder, the car without any adjectives is simply bilen, expressing the definite with the -en postfix and no article involved.
I wish I could tell you which adjectives are irregular, but unfortunately there are no real rules for that. Even with this in mind I am sure you will do great. Good luck!