Летом мы поехали на отдых к морю.

Летом means in summer. It is the instrumental case of лето.

In Russian, names of seasons are very often used in the instrumental to express time:

• зимой = in winter
• весной = in spring
• летом = in summer
• осенью = in autumn

So Летом мы поехали... means In summer, we went...

These forms are related but not the same:

• поехали = went / set off (perfective, one completed trip, usually by transport)
• ехали = were going / went (imperfective, focus on the process)
• ездили = went / used to go / have been (habitual or round-trip sense, often repeated experience)

In this sentence, поехали is used because it describes one completed trip: they went to the seaside for a vacation.

So the sentence presents the trip as a single event in the past.

Historically, yes, поехать can have the idea of to set off or to start going. But in many everyday past-tense sentences, it is simply translated as went.

So here:

• мы поехали к морю = we went to the sea / seaside

You do not always need to translate the starting idea explicitly in English.

In the past tense, Russian verbs show gender and number, but not person.

So поехали only tells you:

• plural
• past tense

It does not by itself tell you whether the subject is:

• we
• they
• or sometimes another plural subject from context

That is why мы is useful here: it makes the subject clear.

На отдых means something like for a vacation, for rest, or on holiday.

This is a common Russian pattern:

• на работу = to work
• на учёбу = to study / to school / to university
• на концерт = to a concert
• на отдых = for a vacation / for отдых

So поехали на отдых means went away for a holiday or went on vacation.

It is accusative case.

With на, Russian can use either:

• accusative for movement toward / purpose
• prepositional for location

Here it is на отдых because it means movement with a purpose: went for a vacation.

Also, for an inanimate masculine noun like отдых, the accusative form looks the same as the nominative:

• nominative: отдых
• accusative: отдых

So the form does not change, but the case is still accusative.

К морю means to the sea / toward the seaside, while на море often means to the seaside as a destination too, but with a slightly different feel.

A simple way to think about it:

• к морю = toward the sea, near the sea, to the coast
• на море = to the seaside / at the seaside

In this sentence, на отдых к морю is a natural expression meaning for a vacation by the sea or to the seaside for a holiday.

So:

• поехать к морю is possible
• поехать на море is also very common

The sentence’s version emphasizes going toward the sea/coast area.

Because к requires the dative case.

The noun is:

• dictionary form: море = sea

After к, it changes to dative singular:

• к морю = to the sea

This is a normal pattern for many neuter nouns ending in -е:

• поле → к полю
• здание → к зданию
• море → к морю

Yes, absolutely. That would be a very common sentence.

Compare:

• Летом мы поехали на море.
  = In summer we went to the seaside.

• Летом мы поехали на отдых к морю.
  = In summer we went to the seaside for a vacation.

The original sentence is a bit fuller and more descriptive because it includes на отдых.

Russian has no articles.

So Russian does not normally distinguish between:

• the sea
• a sea

The exact meaning comes from context.

That is why:

• к морю can be translated as to the sea
• and in good English, often more naturally as to the seaside

No, Russian word order is quite flexible.

The sentence:

• Летом мы поехали на отдых к морю

is a neutral, natural order:

1. time: Летом
2. subject: мы
3. verb: поехали
4. purpose: на отдых
5. destination: к морю

Other orders are possible, for example:

• Мы летом поехали на отдых к морю.
• К морю мы поехали летом на отдых.

These versions may shift emphasis, but the basic meaning stays similar.

A very natural translation would be:

• In summer we went to the seaside for a vacation.
• That summer, we went to the seaside on holiday.
• We went to the sea for a vacation in summer.

A very literal translation is:

• In summer we went for a rest to the sea

But that sounds less natural in English, so went to the seaside for a vacation is usually better.