Veterinären undersöker tassen under återbesöket.

Because Swedish usually marks definiteness by adding an ending to the noun.

• en veterinär = a veterinarian
• veterinären = the veterinarian

So -en here is the definite ending for a common-gender noun.

This is one of the first big differences from English: instead of putting a separate word like the in front, Swedish often attaches definiteness to the end of the noun.

Undersöker is the present tense form of the verb undersöka (to examine).

• att undersöka = to examine
• undersöker = examines / is examining

In Swedish, the present tense often ends in -r.

So:

• Veterinären undersöker tassen = The veterinarian examines the paw

Unlike English, Swedish does not usually need a separate form for examines versus is examining in a basic sentence like this. The present tense can cover both, depending on context.

Because tassen means the paw, while en tass means a paw.

• en tass = a paw
• tassen = the paw

Again, Swedish puts the definite article at the end of the noun:

• tass → tassen

In this sentence, a specific paw is meant, so the definite form is used.

Yes. Tass is the normal word for an animal’s paw.

• tass = paw
• fot = foot

So if you are talking about a dog, cat, or similar animal, tass is the natural choice. Using fot for an animal would usually sound wrong or at least unnatural in ordinary speech.

It is a prepositional phrase:

• under = during / under
• återbesöket = the follow-up visit / the return visit

So under återbesöket means during the follow-up visit.

Here, under is being used in a time sense, not a physical-location sense. It tells you when the examination happens.

It is a compound noun:

• åter- = again / re-
• besök = visit
• återbesök = return visit / follow-up visit
• återbesöket = the follow-up visit

Swedish forms compounds very freely, much more than English. So instead of a multi-word expression, Swedish often prefers one combined noun.

Because Swedish usually expresses definiteness with a suffix attached to the noun.

In this sentence:

• veterinären = the veterinarian
• tassen = the paw
• återbesöket = the follow-up visit

So Swedish does the job of English the by using endings such as -en or -et.

A separate word like den/det/de can also appear in Swedish, but usually only in certain structures, especially with adjectives:

• den stora tassen = the big paw

Without an adjective, just the noun ending is normally enough.

This is the normal Swedish main-clause word order:

Subject + verb + object + other information

So here:

• Veterinären = subject
• undersöker = verb
• tassen = object
• under återbesöket = time phrase

This is very similar to standard English word order: The veterinarian examines the paw during the follow-up visit.

Yes. Swedish is flexible, but moving it changes the word order because of the V2 rule.

You could say:

Under återbesöket undersöker veterinären tassen.

This still means the same thing, but now the time phrase comes first for emphasis. In a Swedish main clause, the finite verb usually stays in the second position, so undersöker must come before veterinären.

That is why you get:

• Under återbesöket undersöker veterinären tassen.

not:

• Under återbesöket veterinären undersöker tassen.

Yes, it matters because gender affects articles and definite endings.

In this sentence:

• en veterinär → veterinären
• en tass → tassen
• ett återbesök → återbesöket

So:

• veterinär is a common-gender noun (en word)
• tass is a common-gender noun (en word)
• återbesök is a neuter noun (ett word)

That is why the definite forms are different:

• common gender often takes -en
• neuter often takes -et

A learner will often notice the vowels ö and å here.

A rough guide:

• ö sounds somewhat like the vowel in French deux or German schön. It is not the same as English o.
• å sounds roughly like the vowel in British English more for many learners, though it is not identical.

Very rough pronunciation help:

• undersöker ≈ UHN-der-shur-ker
• återbesöket ≈ OH-ter-beh-SUR-keht

These are only approximations. The real Swedish sounds are different from English ones, especially ö.

Also note that sj, sk, and similar combinations can be tricky in Swedish, but this sentence does not contain the hardest examples.

It can mean either, depending on context.

Swedish present tense often covers both:

• examines (simple present)
• is examining (present progressive)

So this sentence could be understood as:

• The veterinarian examines the paw during the follow-up visit.
• The veterinarian is examining the paw during the follow-up visit.

English makes a stronger distinction between those two forms than Swedish usually does.

Yes. Under can mean both:

• under/below in a physical sense
• during in a time sense

Examples:

• Katten ligger under bordet. = The cat is lying under the table.
• Under mötet pratade vi om budgeten. = During the meeting, we talked about the budget.

In your sentence, the time meaning is the correct one: under återbesöket = during the follow-up visit.