meistern
to master
To successfully handle a difficult task, challenge, or situation, or to learn a skill perfectly.
Sie hat die schwierige Prüfung mit Bravour gemeistert.
She mastered the difficult exam with flying colors.

to master
Loading your saved state.
to master
To successfully handle a difficult task, challenge, or situation, or to learn a skill perfectly.
Sie hat die schwierige Prüfung mit Bravour gemeistert.
She mastered the difficult exam with flying colors.

The verb 'meistern' (to master) is derived directly from 'der Meister' (the master). So when you master a task, you become the 'Meister' (master) of that task—you have perfect command of it.
Er ist ein wahrer Meister seines Fachs.
He is a true master of his field.
'Meistern' (to master) always takes an accusative object. This object is the difficult thing that one overcomes.
Die Mannschaft hat die schwere Krise erfolgreich gemeistert.
The team successfully mastered the serious crisis.
'Meistern' (to master) is often used with abstract nouns for difficulties. Typical phrases are: 'eine Herausforderung meistern' (to master a challenge), 'eine Krise meistern' (to master a crisis), 'eine Aufgabe meistern' (to master a task), or 'sein Leben meistern' (to master one's life).
Es war nicht einfach, aber sie hat die Herausforderung gemeistert.
It wasn't easy, but she mastered the challenge.
to be able to
'können' and 'meistern' both have to do with ability. 'können' generally says that someone has learned something or is able to do something. 'meistern' is stronger: it means that someone manages a difficult task or has mastered a skill very well. Learners may confuse the words because both speak positively about abilities. For simple abilities, 'können' is usually the right fit. When something was difficult or went especially well, 'meistern' sounds more precise.

Trotz der kurzen Zeit hat das Team die schwierige Aufgabe gemeistert.
Despite the short amount of time, the team mastered the difficult task.
Herr Becker kann gut schwimmen und fährt im Sommer oft an den See.
Mr. Becker can swim well and often goes to the lake in summer.