Недаром учитель посоветовал мне этот словарь: теперь мне легче понимать новые слова.

Here недаром means something like:

• not for nothing
• with good reason
• no wonder

It introduces the idea that what follows is justified by the result after the colon.

In this sentence, Недаром учитель посоветовал мне этот словарь means the teacher’s recommendation turned out to be a good one.

This is different from не даром written as two words, which usually means not free of charge or not without payment.

So:

• недаром = for good reason / not for nothing
• не даром = not for free

Учитель is the subject of посоветовал, so it stays in the nominative.

Structure:

• учитель = the teacher, the person doing the action
• посоветовал = recommended

So учитель посоветовал means the teacher recommended.

The verb посоветовать / советовать commonly takes the person receiving the advice in the dative case.

So:

• посоветовал мне = recommended to me
• literally: advised me

That is why you get мне, not я or меня.

A useful pattern is:

• кто-то посоветовал кому-то что-то
• someone recommended something to someone

In this sentence:

• учитель = someone
• мне = to someone
• этот словарь = something

Этот словарь is the direct object of посоветовал, so it is in the accusative case.

However, for inanimate masculine singular nouns, the accusative looks the same as the nominative.

So:

• nominative: этот словарь
• accusative: этот словарь

That is why the form does not change.

If it were an animate masculine noun, you would see a different pattern more often.

Посоветовал is the perfective past form of посоветовать. It presents the recommendation as a completed single action.

That fits this sentence well: the teacher gave the recommendation, and now we see the result.

Compare:

• учитель посоветовал мне этот словарь = the teacher recommended this dictionary to me
• учитель советовал мне этот словарь = the teacher was recommending / used to recommend this dictionary to me

The perfective form is more natural here because the sentence points to a specific recommendation that had a good result.

The colon introduces the explanation or result of the first part.

Structure:

• first part: Недаром учитель посоветовал мне этот словарь
• second part: теперь мне легче понимать новые слова

The second part explains why it was a good recommendation.

In English, this could often be written with a colon, dash, or even as two separate sentences. In Russian, the colon works very naturally here.

Russian often uses the dative case to express the person who experiences a state or feeling.

So мне легче literally means something like:

• to me, it is easier
• more natural English: it is easier for me

This is a very common Russian pattern:

• мне трудно = it is difficult for me
• ему интересно = it is interesting to him / he is interested
• нам холодно = we are cold

So мне here is not an object of понимать. It is the experiencer of легче.

Легче is the comparative form of легко and means easier.

The pattern is:

• кому-то легче + infinitive
• it is easier for someone to do something

So:

• мне легче понимать = it is easier for me to understand

Russian often prefers this compact comparative structure rather than something more literal like более легко.

After words like легче, Russian often uses an infinitive to say what action is easier.

So:

• мне легче понимать = it is easier for me to understand
• literally: to me [it is] easier to understand

This is a very common structure:

• мне трудно читать = it is hard for me to read
• ему полезно заниматься = it is useful for him to study
• нам приятно видеть вас = it is pleasant for us to see you

This is an aspect question.

• понимать = imperfective
• понять = perfective

Here понимать новые слова means understanding new words in general / repeatedly / as an ongoing ability. The dictionary now helps with that process.

If you said понять, it would sound more like understanding a word as a single completed act, which is not the main idea here.

So понимать is natural because the sentence is about an ongoing improvement in ability.

Новые слова is the object of понимать, so it is in the accusative plural.

But because слова is an inanimate plural noun, its accusative plural looks the same as the nominative plural.

So:

• nominative plural: новые слова
• accusative plural: новые слова

That is why the form does not change.

Yes, Russian word order is flexible, but the original order sounds natural and well-balanced.

Current order:

• Недаром учитель посоветовал мне этот словарь: теперь мне легче понимать новые слова.

This order does a few things well:

• Недаром comes first for emphasis
• учитель appears early as the subject
• теперь introduces the present result clearly

You could rearrange parts, but the emphasis would change. For example:

• Мне теперь легче понимать новые слова. Недаром учитель посоветовал мне этот словарь.

This is also grammatical, but it presents the result first and the justification second. The original sentence is more elegant and explanatory.

By itself, словарь just means dictionary. It does not tell you what kind.

Depending on context, it could be:

• a bilingual dictionary
• a monolingual dictionary
• a specialized dictionary
• even a glossary-like reference work

So the sentence only tells us that it is this dictionary, not what type it is.