Lægen gav mig et plaster, fordi såret på min finger stadig var åbent.

Lægen means the doctor. The ending -en is the usual definite ending for many en-words in Danish.

• en læge = a doctor
• lægen = the doctor

So Danish often attaches the to the end of the noun instead of using a separate word like English does.

Gav is the past tense of give.

• at give = to give
• giver = gives / is giving
• gav = gave
• har givet = has given / have given

It is an irregular verb, so you just have to learn the past form.

Because mig is the object form of I.

• jeg = I (subject form)
• mig = me (object form)

In this sentence, the doctor gave something to me, so Danish uses mig.

• Jeg gav... = I gave...
• Lægen gav mig... = The doctor gave me...

Because plaster is a neuter noun in Danish, so it takes et in the indefinite singular.

• et plaster = a plaster / a bandage / a Band-Aid
• plasteret = the plaster

Danish nouns are divided into grammatical genders, and you usually have to learn each noun with en or et.

Here et plaster means a small adhesive bandage, often like a Band-Aid in English.

So in this sentence it does not mean building plaster or wall plaster. The medical context makes the meaning clear.

Såret means the wound.

• et sår = a wound
• såret = the wound

The definite form is used because it refers to a specific wound: the one on the speaker’s finger. Danish often uses the definite form when the thing is already identifiable from the context.

In Danish, a possessive like min, din, hans, hendes, and so on usually replaces the article.

So you say:

• min finger = my finger
• not den min finger
• not min fingeren

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

Because the adjective agrees with the noun sår, which is a neuter noun.

• en åben dør = an open door
• et åbent sår = an open wound

The base adjective is åben. When it describes a singular et-word, it usually gets -t, so:

• åben → åbent

This is because fordi introduces a subordinate clause, and Danish word order changes in subordinate clauses.

In a main clause, you would normally say:

• Såret var stadig åbent. = The wound was still open.

But after fordi, Danish usually puts adverbs like stadig before the finite verb:

• ... fordi såret på min finger stadig var åbent.

So this is a very common pattern:

• main clause: verb before the adverb
• subordinate clause: adverb before the verb

It has a main clause and a subordinate clause.

Main clause:

• Lægen = subject
• gav = verb
• mig = indirect object
• et plaster = direct object

Subordinate clause:

• fordi = because
• såret på min finger = subject
• stadig var = adverb + verb
• åbent = adjective complement

So the overall pattern is:

[Main clause], fordi [subordinate clause].

Because Danish commonly puts an indirect object pronoun before the direct object.

• Lægen gav mig et plaster. = natural
• Lægen gav et plaster til mig. = possible, but less direct and usually less natural here

So gav mig et plaster is the normal way to say gave me a bandage.

It specifies which wound we are talking about.

• såret = the wound
• på min finger = on my finger

Together:

• såret på min finger = the wound on my finger

This prepositional phrase narrows it down to one particular wound.

Yes. You can also say:

Fordi såret på min finger stadig var åbent, gav lægen mig et plaster.

That is still correct. When the subordinate clause comes first, the main clause still keeps normal Danish main-clause word order, with the finite verb in second position:

• gav comes right after the opening clause.

Yes, in this sentence stadig means still.

• såret ... stadig var åbent = the wound ... was still open

It shows that the wound had not closed yet.