ようやく has the following definitions in
[romajidesu](http://www.romajidesu.com/dictionary/meaning-
of-%E3%82%88%E3%81%86%E3%82%84%E3%81%8F.html):

>   1. ( _adv_ ) **finally; at last**  
>  「そっか」ウィリーはようやく納得した。  
>  "Well, OK," Willie finally agreed.
>
>   2. **barely; narrowly; hardly; only just**  
>  ９時２０分の電車にようやく間に合った。  
>  I barely made the 9:20 train.
>
>   3. **gradually; little by little; by degrees**
>
>

I'm wondering, when is the last definition relevant?

For example, consider the following sentence:

> ようやく理解できたんでしょうね。

Should I read it as "he finally understood what he had to do" or "he gradually
understood what he had to do"?
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grammar translation meaning word-choice
Does ようやく mean "gradually"?
> **ようやく** 理解できたんでしょうね。

I'm not an expert, since I'm also learning how to translate Japanese language
through internet. The biggest problem is so minimum info of the subject, so
just by this line can be translated into many sentences.

`んでしょう` -- can be translated to: I think, I guess, I suppose, probably, it
seems, right?, isn't it, etc.

`できた` -- can be translated to: can, capable, able,etc.

`理解` -- can be translated to: understand, know, realized, comprehend, etc.

So, we need to read the earlier sentences to translate the sentence that you
were asking about.
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> **ようやく** 理解できたんでしょうね。

In this sentence ようやく means "finally" "at last".

"It seems (s/he) finally understood."

* * *

> I'm wondering, when is the last definition relevant?

Here are a few examples using ようやく in the sense of "gradually":

>   * 人々はようやくに列を乱して*（夏目漱石『趣味の遺伝』）--
> [デジタル大辞泉](https://dictionary.goo.ne.jp/jn/226831/meaning/m0u/)
>   * 寒さもようやくゆるんできた --
> [大辞林](https://kotobank.jp/word/%E6%BC%B8%E3%81%8F-653411)
>   * ようやく秋もたけなわになった _Autumn has gradually ripened._ -- プログレッシブ和英中辞典
>

* sounds pretty old-fashioned.

ようやく as "gradually" is usually used with a verb phrase expressing a change of
state, such as ～～てくる, ～～になる.  
ようやく is not very commonly used in this sense in contemporary Japanese. Some
might say it's an outdated usage.
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