It means the firm/company this person works at. 单位Direct translates to Unit. So you could imagine unit as in a unit of a office or a department to help your understanding.

The word 单位 in your sentence means 'workplace, work'. 妈妈去单位加班了---- Mother has gone (to her workplace) to work overtime. 单位 in this meaning is the organization(and its location) one works for(and works in). It's the common case when Chinese learners see the word单位 , they tend to immediately associate it with the word 'unit' in their native languages, and this often creates trouble in getting to its real meaning in Chinese. Generally, the word 单位 in your sentence has no equivelent in foeign languages, or does not mean 'unit' as it seemingly does. In China, a worker or employee has a particular social and legal relationship, different from that in other countries, with the organization they work for.

这里是指工作的地方 翻译时注意看语境

单位：公司/学校/医院/政府部门/等等，上班或工作的群组所在地。 a place with have unit when you go to work.

Means "work place" more like " company" so the setence means " mum went to the work place for the extra work”