das Elternhaus
parental home
The house or apartment in which you grew up with your parents.
Nach dem Studium ist er wieder vorübergehend in sein Elternhaus gezogen.
After university, he temporarily moved back into his parental home.

parental home / family background
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parental home
The house or apartment in which you grew up with your parents.
Nach dem Studium ist er wieder vorübergehend in sein Elternhaus gezogen.
After university, he temporarily moved back into his parental home.

The word is a compound of 'Eltern' (parents) and 'Haus' (house). It literally describes the parents' house, which can refer to the building (meaning 1) or metaphorically to the family influence (meaning 2).
Sein Elternhaus stand in einer kleinen Straße am Stadtrand.
His parental home stood on a small street on the outskirts of town.
You can tell from context whether the building or the upbringing is meant. Verbs like 'wohnen' (to live), 'ausziehen' (to move out), or 'zurückkehren' (to return) point to the building. Adjectives like 'musikalisch' (musical), 'streng' (strict), or 'liberal' (liberal) and verbs like 'stammen aus' (to come from) point to the upbringing.
Mit 19 Jahren ist sie von zu Hause ausgezogen.
She moved out of home at the age of 19.
When the physical house is meant, it is often combined with verbs of movement or living: 'aus dem Elternhaus ausziehen' (to move out of one's parental home), 'ins Elternhaus zurückkehren' (to return to one's parental home), or 'noch im Elternhaus wohnen' (to still live in one's parental home).
Viele Studenten wohnen während des Studiums noch im Elternhaus.
Many students still live in their parental home during their studies.
When the family influence is meant, someone's origin is often described. Typical formulations are 'aus einem ... Elternhaus stammen' (to come from a ... family background) or 'vom Elternhaus geprägt sein' (to be shaped by one's family background).
Ihre Liebe zur Literatur wurde durch ihr Elternhaus geprägt.
Her love of literature was shaped by her family background.
homeland / home
'die Heimat' and 'das Elternhaus' can both be connected with childhood and origin. However, 'Heimat' is broader and means a place, region, or country to which you have a strong attachment. 'Elternhaus' means either the actual house or apartment where you grew up with your parents, or the family background that shaped you during that time. The words can be confused because both bring back memories of the past. If it is about the larger place or the feeling of belonging, 'Heimat' fits. If it is about the family, upbringing, or childhood home, 'Elternhaus' fits.

Selma besucht am Wochenende ihr Elternhaus und hilft ihrem Vater im Garten.
Selma visits her parental home on the weekend and helps her father in the garden.
Nach dem Umzug fühlt sich Tom in der neuen Stadt noch nicht wie in seiner Heimat.
After moving, Tom does not yet feel as at home in the new city as he did in his homeland.