This is the 538th most frequent Hungarian word.
végére
"Végére" means "to the end" in English.
In this sentence, 'végére' is used to indicate arriving at the conclusion or endpoint of something, in this case, a story.
Elérkeztünk a történet végére.
We have reached the end of the story.
Here, 'végére' specifies the end point or destination of the journey described.
A futó az útszakasz végére ért.
The runner reached the end of the section of the road.
In this sentence, 'végére' is used metaphorically to indicate the final part of a process or timeframe.