De trainer laat de groep een rondje om het plein heen lopen.

It is a causative construction with laten.

• laten + object + infinitive means to have/make/let someone do something
• So De trainer laat de groep ... lopen means:
  • The trainer has the group walk ...
  • or The trainer makes the group walk ...
  • or sometimes The trainer lets the group walk ...

Which English translation sounds best depends on context. In a training situation, has the group walk is often the most natural.

Because after laten, Dutch normally puts the second verb in the infinitive, and that infinitive usually goes to the end of the clause.

So the structure is:

• De trainer = subject
• laat = finite verb
• de groep = object
• een rondje om het plein heen = more information
• lopen = infinitive at the end

This is very common in Dutch with verb combinations:

• Ik wil gaan.
• Zij kan zwemmen.
• De trainer laat de groep lopen.

Because after laten, Dutch uses a bare infinitive.

So you say:

• De trainer laat de groep lopen.

Not:

• De trainer laat de groep te lopen.

This is similar to English make/let someone do something, not make/let someone to do something.

Other verbs that often take a bare infinitive include:

• zien: Ik zie hem lopen.
• horen: Ik hoor haar zingen.
• voelen: Ik voel het trillen.

Een rondje is the diminutive form of ronde or related to rond/round, and it often means:

• a little round
• a lap
• a circuit
• a short loop

In this sentence, een rondje om het plein heen lopen means to walk one lap around the square.

The diminutive -je often makes a word sound:

• smaller
• more informal
• lighter in tone

So een rondje feels very natural here, like a lap rather than something overly formal.

Om ... heen means around.

So:

• om het plein heen = around the square

Dutch often uses this combination to express movement around something:

• om het huis heen lopen = walk around the house
• om de tafel heen gaan = go around the table

Why both words?

• om gives the idea of around
• heen reinforces the idea of movement along that path

In many sentences, heen is very natural or even expected. It makes the expression feel complete.

Yes, sometimes you can, but the meaning may feel a bit less explicit or slightly different depending on context.

• om het plein heen lopen clearly means walk around the square
• om het plein lopen can also mean that, but heen makes the route more clearly circular/around it

In practice, for a learner, om ... heen is a very good pattern to remember for around in a physical sense.

Because de groep is the direct object of laten.

The structure is:

• De trainer lets/makes
• de groep do something

So de groep is the thing/person being caused to act.

Compare:

• De trainer laat de groep lopen. = The trainer has the group walk.

You do not use aan here, because the group is not an indirect object like to the group. It is the group that performs the action lopen.

It can cover both ideas, which is why it sometimes feels tricky for English speakers.

Laten can mean:

• let = allow
• make/have = cause or instruct

In this sentence, because it is a trainer giving an exercise, English often prefers:

• The trainer has the group walk a lap around the square
• or The trainer makes the group walk a lap around the square

If the context is more permissive, lets could work, but here has is probably the best neutral choice.

Yes. This is a normal main clause in Dutch, and Dutch main clauses usually follow V2 word order:

• first position: one element
• second position: the finite verb

Here:

• De trainer = first position
• laat = second position

So the sentence starts in the most neutral way:

• De trainer laat de groep ... lopen.

You could move another element to the front for emphasis, but then the verb still stays second:

• Een rondje om het plein heen laat de trainer de groep lopen. This is grammatical, but much less neutral.

Because Dutch nouns have different grammatical genders/article classes:

• de trainer
• de groep
• het plein

Unfortunately, this is something you often have to learn with each noun.

A few helpful points:

• many people-words take de: de trainer, de student, de man
• diminutives always take het, but that does not apply here because plein is not a diminutive
• plein just happens to be a het-word

So:

• de trainer
• de groep
• het plein

Yes. Om ... heen is a kind of split expression.

The noun phrase goes in the middle:

• om het plein heen
• om de tafel heen
• om het gebouw heen

This is very common in Dutch with preposition-like combinations:

• naar binnen
• naar buiten
• om ... heen
• door ... heen

So in om het plein heen, the thing you go around (het plein) naturally appears between om and heen.

Yes, something like that is possible, but om het plein heen is the more standard and clearer way to say around the square.

• rond het plein can also mean around the square
• but om het plein heen strongly emphasizes movement around it

So for a learner, een rondje om het plein heen lopen is an excellent, natural phrase to remember.

Yes, it is very natural.

It sounds like something you might hear:

• in sports training
• at school
• during a group exercise
• in a fitness or coaching context

It has a very normal spoken-Dutch feel:

• De trainer = the trainer/coach
• laat de groep = has the group
• een rondje = a lap
• om het plein heen lopen = walk around the square

So it is a good model sentence for learning both laten + infinitive and om ... heen.