Na stubištu sam jutros susrela susjedu koja živi kat iznad nas.

Croatian often forms the past tense with:

• the present tense of biti (to be) as an auxiliary, plus
• the past participle of the main verb.

So:

• sam = I am (auxiliary here, not full am)
• susrela = past participle of susresti (to meet / run into)

Together, sam susrela means I met.

This is the normal Croatian past tense pattern:

• vidjela sam = I saw
• došla je = she came
• kupili smo = we bought

Notice that in Croatian, the auxiliary often comes in second position in the sentence, which is why you get Na stubištu sam jutros susrela...

The form susrela shows that the speaker is female.

In Croatian, the past participle agrees with the subject in gender and number:

• susreo sam = I met (male speaker)
• susrela sam = I met (female speaker)

So this sentence tells you the speaker is a woman.

Because susjedu is the accusative singular form of susjeda / susjeda? Actually, the basic noun here is susjeda = female neighbor.

After the verb susresti (to meet), the person you meet is a direct object, so Croatian uses the accusative:

• nominative: susjeda = the neighbor
• accusative: susjedu = the neighbor (as object)

So:

• Susjeda živi ovdje. = The neighbor lives here.
• Srela sam susjedu. = I met the neighbor.

In this sentence, susrela most naturally means met or ran into.

The verb susresti / sretati usually means meeting someone, often by chance. In everyday English, ran into is often a very natural translation here.

So:

• Na stubištu sam jutros susrela susjedu...
  = I ran into / met my neighbor on the stairs this morning...

It does not mean met for the first time. For that idea, Croatian would use something more like upoznati.

Na stubištu means on the staircase / in the stairwell.

Here:

• na is a preposition
• stubištu is locative singular of stubište (staircase, stairwell)

With location, na often means on / at, and it takes the locative:

• na stolu = on the table
• na poslu = at work
• na stubištu = on the stairs / in the stairwell

A learner may wonder why English says on the stairs but Croatian uses a form that can also feel like in the stairwell. Croatian and English divide space a bit differently here. Na stubištu is perfectly normal.

This is because Croatian has a strong tendency for clitics—short unstressed words like sam, si, je, smo, su—to appear in the second position of the clause.

So in:

• Na stubištu sam jutros susrela susjedu...

the word sam comes early, after the first sentence element Na stubištu.

This does not change the meaning. Croatian word order is more flexible than English, but clitics have placement rules.

You could compare:

• Jutros sam susrela susjedu.
• Na stubištu sam susrela susjedu.

In both, sam tends to come second.

Jutros is an adverb, and it means this morning.

It is used very often in Croatian:

• Jutros sam rano ustao. = I got up early this morning.
• Jesi li jutros doručkovao? = Did you have breakfast this morning?

So in the sentence:

• Na stubištu sam jutros susrela...
  = I met ... on the stairs this morning.

Koja is a relative pronoun meaning who / which / that.

It refers back to susjedu (the female neighbor), so it must match it in gender and number:

• koja = feminine singular
• because susjeda / susjedu is feminine singular

So:

• susjedu koja živi kat iznad nas
  = the neighbor who lives one floor above us

If it referred to a masculine noun, you would get koji:

• susjeda koji živi... = the male neighbor who lives...

Because the relative clause describes a general, ongoing fact about the neighbor, not a one-time past event.

Main clause:

• sam susrela = I met (past event)

Relative clause:

• koja živi kat iznad nas = who lives one floor above us (current/general fact)

This is very natural in both Croatian and English:

• I met the neighbor who lives above us.

You would not normally say who lived above us unless that was true only in the past.

Kat iznad nas literally means a floor above us or one floor above us.

• kat = floor/story
• iznad = above
• nas = us

In Croatian, it is common to say simply kat iznad without explicitly adding jedan (one), just as English often says a floor above us.

So:

• živi kat iznad nas
  = she lives one floor above us

It is an idiomatic, everyday way to say it.

The preposition iznad (above) takes the genitive case.

The pronoun mi (we) changes in the genitive to nas:

• nominative: mi = we
• genitive: nas = of us / us (after certain prepositions)

So:

• iznad nas = above us
• pored nas = next to us
• kod nas = at our place / with us

This is just standard case government after the preposition iznad.

Yes. Croatian usually omits subject pronouns when they are not needed.

The form sam susrela already tells you the subject is I, and susrela also tells you the speaker is female. Because of that, Croatian does not need to say ja.

So:

• (Ja) sam jutros susrela susjedu.
  = I met the neighbor this morning.

Adding ja is possible, but it gives extra emphasis:

• Ja sam jutros susrela susjedu. = I met the neighbor this morning.

Yes. Croatian word order is fairly flexible, although some orders sound more neutral than others and clitics like sam still have placement rules.

For example, these are all possible with slight differences in focus:

• Jutros sam na stubištu susrela susjedu...
• Susjedu koja živi kat iznad nas jutros sam susrela na stubištu.
• Na stubištu sam jutros susrela susjedu...

The original sentence is very natural. It starts with Na stubištu, which gives the setting first, then sam appears in second position as expected.