This sentence literally means 'She had (gaeth hi) her hearing (ei chlywed)'.
It's the simplest way Welsh expresses the passive voice.
The pattern is the same for such sentences as:-
'She was born' (Gaeth hi ei geni - She had her birth)
'She was brought up' (Gaeth hi ei magu - She had her upbringing)
'She was paid' - (Gaeth hi ei thalu - She had her paying)
I've just added another sentence to this lesson:-
'She was heard by Megan' (Gaeth hi ei chlywed gan Megan - She had her hearing by Megan)
Hope that clarifies things.