Za domem je pole.

Because the preposition za changes case depending on meaning.

• za + instrumental = location, behind
• za + accusative = motion, to behind / behind toward

So in Za domem je pole, the field is already located behind the house, so Czech uses the instrumental: domem.

Compare:

• Za domem je pole. = The field is behind the house.
• Jdu za dům. = I am going behind the house.

Domem is the instrumental singular of dům (house).

A learner often meets dům first as the dictionary form, which is the nominative singular. But after za in a location meaning, it changes to instrumental:

• dům → nominative
• domem → instrumental

So za domem is a prepositional phrase meaning behind the house.

This is a very common Czech pattern: some prepositions take different cases depending on whether you are talking about location or direction.

With za:

• instrumental = where something is
• accusative = where something is going

Here, the sentence describes a position, not movement, so Czech uses the instrumental:

• Za domem je pole. = The field is behind the house.
• Jedu za dům. = I am driving behind the house.

This location-vs-motion distinction is very important in Czech.

Because Czech has no articles. It does not have words like the or a/an.

So:

• dům can mean a house or the house
• pole can mean a field or the field

The exact meaning depends on context. In English, you must choose a or the. In Czech, you usually do not.

Because pole is the subject of the sentence, and subjects normally appear in the nominative case, which is the dictionary form.

In Za domem je pole:

• za domem = behind the house
• je = is
• pole = field

So pole is nominative singular.

Also, pole is a neuter noun.

Both are possible, but they sound a little different in focus.

• Pole je za domem. = The field is behind the house.
  
  • good if you are talking about the field
• Za domem je pole. = Behind the house, there is a field.
  
  • good if you are introducing what is behind the house

Czech word order is more flexible than English, and it often reflects information structure:

• what is already known or the setting often comes earlier
• the new or important information often comes later

So Za domem je pole can sound natural when answering something like What is behind the house?

Yes, literally it is something like Behind the house is a field.

Czech does not need a dummy subject like English there in there is/there are. English says:

• There is a field behind the house.

Czech can simply say:

• Za domem je pole.

So the idea of there is is often expressed just by normal Czech word order and the verb je.

Je is the 3rd person singular present form of být (to be).

So:

• já jsem = I am
• ty jsi = you are
• on/ona/ono je = he/she/it is

In this sentence, je agrees with pole, which is singular:

• Za domem je pole. = There is a field behind the house.

If the subject were plural, the verb would also be plural:

• Za domem jsou pole. = There are fields behind the house.

Yes, it matters.

• dům is masculine inanimate
• pole is neuter

Gender affects things like:

• adjective endings
• pronouns
• some verb agreement patterns
• case endings

In this sentence, you mainly see gender through the noun forms:

• dům → domem in the instrumental singular
• pole stays pole in the nominative singular

Knowing the gender helps you decline the nouns correctly in other sentences.

Yes, but the meaning changes slightly depending on the noun.

• pole = field
• políčko = little field / small plot

So Za domem je pole is a neutral, normal statement.
If you change the noun, you change the nuance, but the grammar pattern stays the same:

• Za domem je políčko.

A simple learner-friendly pronunciation is:

za DO-mem ye PO-le

A bit more carefully:

• za = like za in pizza, but short
• domem = DO-mem
• je = roughly ye
• pole = PO-le

Stress in Czech normally falls on the first syllable of each word:

• ZA
• DOmem
• je
• POle

Also, Czech j is pronounced like English y in yes.

Normally, no. In a full standard sentence like this, je should be there.

So:

• Za domem je pole. = correct
• Za domem pole. = not a normal complete standard sentence

Czech sometimes omits forms of to be in very informal speech, headlines, notes, or special styles, but learners should keep je here.

They are:

• za = preposition
• dům = house
• být = to be
• pole = field

In the sentence, only dům changes form:

• dictionary form: dům
• sentence form: domem

That is a very normal thing in Czech, because endings change according to case.