De breve minder mig om min bedstemor, så jeg gemmer dem i en mappe.

Both can mean the letters, but they are used a little differently.

• brevene is the normal definite plural form: the letters
• de breve is the preposed definite form: literally those/the letters

In Danish, when a noun has a determiner like de, den, det, or an adjective before it, the noun usually appears in its indefinite-looking form:

• brevene = the letters
• de breve = the letters / those letters

In this sentence, de breve refers to a specific set of letters already understood from context.

Because dem is the object form of de.

• de = subject form, like English they
• dem = object form, like English them

So:

• De breve minder mig om min bedstemor = Those letters remind me of my grandmother
• jeg gemmer dem = I keep/save them

English also has this distinction:

• they remind me
• I keep them

The verb pattern is:

noget minder nogen om noget/nogen

That means:

something reminds someone of something/someone

So here:

• De breve = the thing doing the reminding
• minder = reminds
• mig = me
• om min bedstemor = of my grandmother

So the structure is very close to English, except Danish uses om very naturally in this expression.

Example:

• Det minder mig om min barndom = It reminds me of my childhood

Because when you use a possessive like min, the noun does not take the normal definite ending.

Compare:

• bedstemor = grandmother
• bedstemoren = the grandmother
• min bedstemor = my grandmother

This is similar to English: we say my grandmother, not my the grandmother.

So min already makes the noun specific, and no extra definite ending is added.

Here så means so or therefore.

It connects the two ideas:

• The letters remind me of my grandmother
• so I keep them in a folder

Danish så can have several meanings depending on context, including:

• so / therefore
• then
• so as an intensifier in some contexts

In this sentence, it clearly means therefore / so.

Both can exist, but they are not used in exactly the same way.

In this sentence, så is working as a coordinating conjunction meaning so, joining two main clauses:

• De breve minder mig om min bedstemor
• så jeg gemmer dem i en mappe

That is why the second clause keeps normal main-clause word order:

• jeg gemmer dem

If så is used more like an adverb at the beginning of a main clause, then inversion is common:

• Så gemmer jeg dem i en mappe = Then/so I keep them in a folder

So the version in your sentence is natural because it is linking two full clauses.

Gemmer comes from at gemme, which often means:

• to keep
• to save
• to store
• to put away

It can sometimes also mean to hide, depending on context.

Here, because of i en mappe (in a folder), the meaning is more like:

• I keep them
• I store them
• I save them

So it is not necessarily secretive; it just means the speaker keeps the letters carefully.

Mappe usually means a folder, file, or sometimes a binder-like folder, depending on context.

So i en mappe means:

• in a folder
• in a file

The preposition i means in.

And en is used because mappe is a common-gender noun:

• en mappe
• mappen = the folder

There actually is definiteness there: it is carried by de.

• brev = letter
• breve = letters
• de breve = the letters / those letters

So even though breve itself does not have the ending -ne, the phrase is still definite because of de.

This is a normal Danish pattern:

• de store huse = the big houses
• de breve = the letters

Yes, bedstemor is a standard and very common word for grandmother.

You may also hear family-specific forms such as:

• mormor = maternal grandmother
• farmor = paternal grandmother

So:

• min bedstemor = my grandmother in a general sense
• min mormor = my mother’s mother
• min farmor = my father’s mother

If the speaker says bedstemor, they may simply be speaking generally or using the family’s preferred term.

A natural singular version would be:

Dette brev minder mig om min bedstemor, så jeg gemmer det i en mappe.

Notice the changes:

• De breve → Dette brev = this letter
• dem → det = it

That happens because brev is a neuter noun:

• et brev
• dette brev
• det

So the pronoun must match the noun’s gender and number.