Cum legatus appropinquaret, puer parvus primus eum agnovit et matri monstravit.

Here cum means when in a past narrative setting, and it often introduces a circumstantial or temporal clause with the subjunctive.

So:

• cum legatus appropinquaret = when / while the envoy was approaching

The verb is in the imperfect subjunctive because the main verb is in past time and the clause gives background information. This is a very common pattern in Latin storytelling.

Appropinquaret is imperfect subjunctive active, 3rd person singular, from appropinquare.

You can understand it as:

• was approaching
• approached, in the sense of background action
• when the envoy was coming near

The imperfect here suggests an action in progress in the past, setting the scene for what follows.

Legatus is a noun meaning envoy, ambassador, deputy, or sometimes lieutenant, depending on context.

In this sentence it is:

• nominative singular masculine
• the subject of appropinquaret

So legatus appropinquaret means the envoy was approaching.

Both word orders are possible in Latin.

• puer parvus
• parvus puer

Both mean the small boy or the little boy.

Latin word order is more flexible than English because endings show how words function. Here puer and parvus are both:

• nominative
• singular
• masculine

so they clearly go together.

The order puer parvus may put the noun first and then describe him, but it does not change the basic meaning.

Primus means first.

It agrees with puer:

• nominative
• singular
• masculine

So the phrase means:

• the little boy was the first to recognize him

Latin often uses primus with a finite verb where English might say was the first to...

So:

• puer parvus primus eum agnovit
  = the little boy recognized him first
  or more literally
  = the little boy was the first to recognize him

Eum is the accusative singular masculine form of is, meaning him.

It refers back to legatus.

So:

• eum agnovit = he recognized him
• eum ... monstravit = he showed him

Latin often uses pronouns like this to refer back to someone already mentioned.

Matri is the dative singular of mater, meaning mother.

The verb monstrare can take:

• a direct object = the thing shown
• a dative = the person to whom it is shown

So:

• eum matri monstravit = he showed him to his mother

This is very natural Latin.

Because Latin often expresses to someone simply with the dative case, without any preposition.

In English we say:

• to his mother

In Latin, the ending itself does that job:

• matri

So the dative often covers meanings like:

• to
• for

depending on context.

It usually means something stronger than just saw.

Agnovit comes from agnoscere, which means:

• recognize
• identify
• come to know

So the idea is not merely that the boy noticed the envoy, but that he recognized who he was.

Both are perfect indicative active, 3rd person singular.

• agnovit = recognized
• monstravit = showed

In this sentence, the cum clause gives background:

• when the envoy was approaching

Then the perfect verbs give the main actions that happened:

• the little boy recognized him
• and showed him to his mother

This is a very common Latin narrative pattern:

• background action in the imperfect/subjunctive
• main completed actions in the perfect

Yes.

Latin often does not repeat the subject if it is clear. Once puer parvus has been introduced, the verbs agnovit and monstravit are understood to have the same subject:

• the little boy recognized him and showed him to his mother

So there is no need for Latin to repeat puer.

In other contexts, yes, cum can mean different things, such as:

• when
• since
• although

But here the most natural meaning is when or while, because the clause gives the time/background for the main action.

So in this sentence:

• cum legatus appropinquaret
  most naturally means
  when the envoy was approaching

Because appropinquare usually means to approach in the sense of to come near, and in Latin it is often used with the dative for the person or thing approached, or with no expressed object if the context is enough.

Here no object is stated, so the sentence simply means:

• the envoy was approaching
• the envoy was coming near

The focus is on his movement toward the scene, not on specifying exactly whom or what he was approaching.

The word order helps with emphasis, but the grammar is mainly shown by endings.

A learner might rearrange it mentally like this:

• Cum legatus appropinquaret, puer parvus eum primus agnovit et eum matri monstravit.

Or in smoother English order:

• When the envoy was approaching, the little boy recognized him first and showed him to his mother.

Latin puts words where the writer wants them for rhythm or emphasis, but the case endings keep the sentence understandable.