This is a very eloquent section of the work. Just to set the stage a bit, this is the part of the story where Beowulf killed Grendel in a battle. A good paraphrase would be something like this.
Beowulf killed Grendel and sent him to the place where the dead go. For this reason one of the great enemies of humanity has been rid of. However, this was not the end of the problem, because Grendel's mother was now aflame with sorrow and more importantly rage. What she, therefore, was looking for was revenge. We can say that it was pay back time. So, she made a journey to the place of the Danes to get even.
To give even a shorter paraphrase, we can say: Beowulf killed Grendel, which caused Grendel's mother to seek revenge. So, she came to get even.