Esimies käski minua odottamaan.

Käski is the past tense of käskeä.

• käskeä = to order, command, tell someone to do something
• hän käskee = he/she tells or orders
• hän käski = he/she told or ordered

So Esimies käski... means that the boss/supervisor gave the order in the past.

Because käskeä normally uses this pattern:

käskeä + person in the partitive + verb in the -maan/-mään form

So:

• minua = me, in the partitive
• odottamaan = to wait, in the form required by this construction

This is just the normal grammar of the verb here.
So Finnish says, in effect:

• Esimies käski minua odottamaan.

not normally:

• Esimies käski minä odottamaan. ❌
• Esimies käski minut odottamaan. ❌ in standard Finnish

For an English speaker, it helps to learn this as a set pattern rather than trying to map it word-for-word.

Odottamaan is the third infinitive illative form of odottaa.

You will often hear this called the -maan/-mään form.

• odottaa = to wait
• odottamaan = to wait / into waiting, in a structure after certain verbs

This form is very common after verbs that involve:

• telling someone to do something
• going to do something
• starting or leaving something to do something

For example:

• mennä syömään = go eat
• jäädä odottamaan = stay and wait
• käskeä joku odottamaan = tell someone to wait

So here odottamaan is not random; it is the form that käskeä requires in this kind of sentence.

Because after käskeä, Finnish does not normally use the basic infinitive odottaa in this structure.

English uses:

• tell someone to wait

Finnish uses:

• käskeä jotakuta odottamaan

So where English has to wait, Finnish uses the -maan/-mään form instead.

That is one of the big differences between English and Finnish: Finnish often expresses the idea of English to + verb with a special infinitive form rather than a separate word like to.

It can be translated as either, depending on context, but käskeä is usually fairly strong.

It often suggests:

• authority
• a command
• an instruction

So ordered is often closer to the literal force of the Finnish verb.

However, in everyday English, The boss told me to wait may sound more natural than The boss ordered me to wait, even if the Finnish verb is käski.

So the difference is mostly about tone in translation, not grammar.

Historically, mies means man, so that is a very natural question.

In actual usage, esimies has traditionally meant supervisor / boss regardless of gender. So it has often been used as a gender-neutral job title, even though the word contains mies.

That said, many speakers today prefer esihenkilö, which is more clearly gender-neutral.

So:

• esimies = traditional and still common
• esihenkilö = newer, more explicitly gender-neutral

Both can mean supervisor.

Yes, Finnish word order is fairly flexible, but changing it can change the emphasis.

The neutral order here is:

• Esimies käski minua odottamaan.

If you say:

• Minua esimies käski odottamaan.

it still means the same thing, but now minua is emphasized, roughly like:

• It was me that the boss told to wait.

However, word order can also affect how words are grouped. For example, if minua were placed after odottamaan, it could start sounding like wait for me, because odottaa can take an object in the partitive.

So yes, Finnish word order is flexible, but not completely free.

Yes. This is a very useful pattern to memorize:

käskeä + partitive person + -maan/-mään form

For example:

• Opettaja käski oppilaita istumaan.
  The teacher told the students to sit down.

• Äiti käski minua tulemaan heti kotiin.
  Mom told me to come home immediately.

• Esimies käski minua odottamaan.
  The boss told me to wait.

If you learn the whole pattern, it will feel much easier than trying to build it from English every time.