nebenher
on the side
In addition to a main activity or main job; as a side job or secondary activity.
Sie studiert Medizin und arbeitet nebenher als Kellnerin.
She is studying medicine and works as a waitress on the side.

on the side / meanwhile
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on the side
In addition to a main activity or main job; as a side job or secondary activity.
Sie studiert Medizin und arbeitet nebenher als Kellnerin.
She is studying medicine and works as a waitress on the side.

The adverb 'nebenher' consists of 'neben' (beside/alongside) and 'her' (here/from there). It literally describes an action that 'runs alongside' another one, meaning it happens at the same time or additionally.
Beim Aufräumen habe ich nebenher ein Hörbuch gehört.
While tidying up, I listened to an audiobook at the same time.
'Nebenher' can stand at the beginning of a sentence and then triggers inversion (verb in position 2). It can also be placed flexibly within the sentence.
Nebenher verdient er sich mit Fotografie etwas Geld.
On the side, he earns some money with photography.
The exact meaning depends on the context. If it is about work or study, it means 'als Nebenjob' (as a side job). If it is about everyday actions, it means 'beiläufig zur gleichen Zeit' (casually at the same time).
Er ist Student und jobbt nebenher in einem Café.
He is a student and works part-time in a café on the side.
In the meaning 'als Nebenbeschäftigung' (as a secondary activity), 'nebenher' is often combined with verbs such as 'arbeiten' (to work), 'jobben' (to work a casual job), 'studieren' (to study), or 'Geld verdienen' (to earn money).
Viele Künstler müssen nebenher arbeiten, um leben zu können.
Many artists have to work on the side in order to make a living.
simultaneously / at the same time
'gleichzeitig' and 'nebenher' can both mean that two things happen at the same time. The difference lies in the focus. 'gleichzeitig' only says that something happens in the same moment or in addition; it does not evaluate the activities. 'nebenher', on the other hand, sounds as if there is a main activity and a second thing that you do additionally or rather casually. Learners may confuse the words because both have to do with simultaneity. If both things are equally important, 'gleichzeitig' fits better. If something only happens alongside a main activity, 'nebenher' is more natural.

Yusuf hört beim Kochen nebenher einen Podcast.
Yusuf listens to a podcast on the side while cooking.
Die Chefin telefoniert und liest gleichzeitig die neuen Zahlen.
The boss is talking on the phone and reading the new figures at the same time.