Бабушка сказала детям не трогать улей, потому что пчёлы могут больно жалить.

Детям is dative plural of дети (children).

After сказать, the person you say something to is usually in the dative case:

• сказать кому? = to say to whom?
• сказала детям = she told the children

So in this sentence:

• Бабушка сказала детям... = Grandma told the children...

This is different from English, where children stays the same form.

In Russian, after verbs like сказать, it is common to use an infinitive to express an instruction, command, or prohibition.

So:

• сказала детям не трогать улей
  literally: told the children not to touch the hive

This is a very normal Russian pattern:

• Мама сказала мне подождать. = Mom told me to wait.
• Учитель сказал нам молчать. = The teacher told us to be quiet.

A fuller alternative is also possible:

• Бабушка сказала детям, чтобы они не трогали улей.

That version is a bit more explicit, but the infinitive version is shorter and very natural.

Because this is not a full separate clause like the children do not touch. It is the content of what Grandma told them.

Compare:

• Дети не трогают улей. = The children are not touching / do not touch the hive.
• Бабушка сказала детям не трогать улей. = Grandma told the children not to touch the hive.

So не трогать is an infinitive meaning not to touch.

Трогать is the imperfective verb, and here it sounds natural because the idea is a general prohibition: don’t touch it / keep your hands off it.

• трогать = to touch, be touching
• тронуть = to touch once, to make contact once

With warnings and prohibitions, Russian often prefers the imperfective when the meaning is general or ongoing:

• Не курить. = No smoking.
• Не шуметь. = Do not make noise.
• Не трогать. = Do not touch.

Не тронуть is possible in some contexts, but it is much less natural here. It sounds more like not to touch even once as a single completed act. For a general warning on something dangerous, не трогать is the usual choice.

Улей is in the accusative singular, because it is the direct object of трогать:

• трогать что? = to touch what?
• трогать улей = to touch the hive

The reason it looks unchanged is that улей is masculine and inanimate, and for masculine inanimate nouns, the accusative singular is usually the same as the nominative singular.

So:

• nominative: улей
• accusative: улей

If it were animate, the accusative would often look different.

Потому что means because.

It introduces the reason:

• Бабушка сказала детям не трогать улей, потому что...
• Grandma told the children not to touch the hive, because...

The comma is standard in Russian before потому что, since it introduces a subordinate clause.

Very literally:

• потому = therefore / for that reason
• что = that

But as a fixed expression, just think of it as because.

Because пчёлы is the subject of the clause:

• пчёлы могут больно жалить = bees can sting painfully

The subject of a clause is normally in the nominative case.

Singular and plural:

• пчела = bee
• пчёлы = bees

So the second part of the sentence has:

• пчёлы = subject
• могут = verb
• жалить = infinitive after the modal verb
• больно = adverb-like word meaning painfully

Могут is the plural form of мочь (can / to be able to).

Russian modal verbs often work like this:

• conjugated modal verb + infinitive

So:

• пчёлы могут жалить = bees can sting

Compare:

• Я могу помочь. = I can help.
• Они могут прийти. = They can come.

Since пчёлы is plural, we use могут, not может.

Here больно means painfully or in a way that hurts.

So:

• больно жалить = to sting painfully
• more natural English: to sting badly, to give painful stings

This word is very common in Russian. You may also know it as:

• Мне больно. = It hurts / I’m in pain.

In this sentence, it functions like an adverb describing жалить.

Because жалить is the normal Russian verb for what bees, wasps, and similar insects do: to sting.

So:

• пчела жалит = a bee stings
• оса жалит = a wasp stings

This is different from:

• кусать = to bite

A bee does not кусать here; it жалит.

Yes. Russian word order is more flexible than English, because cases show the grammatical roles.

The original sentence is neutral and natural:

• Бабушка сказала детям не трогать улей, потому что пчёлы могут больно жалить.

But other orders are possible for emphasis, for example:

• Детям бабушка сказала не трогать улей...
  puts more emphasis on the children
• Улей бабушка сказала детям не трогать...
  strongly emphasizes the hive

Even though Russian allows this flexibility, the original order is probably the best for a learner to use.

Yes. Russian сказать can correspond to both English say and tell, depending on structure and context.

Here, because we have:

• сказала детям = said to the children / told the children

the best English translation is usually told.

Compare:

• Бабушка сказала: ... = Grandma said: ...
• Бабушка сказала детям не трогать улей. = Grandma told the children not to touch the hive.

So the Russian verb stays the same, but English chooses either said or told.

Grammatically, могут most directly means can or are able to:

• пчёлы могут больно жалить = bees can sting painfully

But in context, English may translate this more naturally as:

• because bees can sting badly
• because bees might sting
• because bees may sting and it hurts

So the core Russian meaning is can, but natural English sometimes uses might because the sentence is giving a warning about possible danger.

Yes, it is natural and clear.

A Russian speaker might also say similar versions such as:

• Бабушка сказала детям не трогать улей: пчёлы больно жалят.
• Бабушка велела детям не трогать улей, потому что пчёлы могут ужалить.

But your sentence is perfectly normal.

A small vocabulary note:

• жалить = to sting
• ужалить = to sting once

So могут больно жалить suggests a general danger, while могут ужалить suggests a possible single sting event. Both make sense.