die Heimreise
journey home
The trip or route back home or to the starting point of a journey.
Nach einem langen Urlaub traten wir am Sonntag die Heimreise an.
After a long vacation, we began the journey home on Sunday.

journey home
Loading your saved state.
journey home
The trip or route back home or to the starting point of a journey.
Nach einem langen Urlaub traten wir am Sonntag die Heimreise an.
After a long vacation, we began the journey home on Sunday.

The word is made up of 'Heim' (home) and 'Reise' (journey). So it literally describes a journey home.
Die Heimreise nach dem langen Urlaub war sehr entspannt.
The journey home after the long vacation was very relaxed.
'Heimreise' (journey home) is often used with the verb 'antreten' (to begin/set out on) in the fixed expression 'die Heimreise antreten' (to begin the journey home). Another common combination is 'sich auf die Heimreise machen' (to set off on the journey home).
Nach der Konferenz traten die Teilnehmer die Heimreise an.
After the conference, the participants began the journey home.
The phrase 'die Heimreise antreten' (to begin the journey home) sounds somewhat more formal and is frequently used in written texts or reports. In everyday life, people often simply say 'nach Hause fahren' (to drive/go home) or 'zurückfliegen' (to fly back).
Die Delegation trat am Abend die Heimreise an.
The delegation began the journey home in the evening.
return
'die Rückkehr' and 'die Heimreise' can both mean that someone comes back home or to a starting point. However, 'die Heimreise' emphasizes the journey or trip home, for example after a vacation. 'die Rückkehr' more strongly emphasizes arriving or being back. The words can be confused because both have to do with coming back. If you are talking about the trip, 'Heimreise' fits better. If you are talking about the moment or fact of coming back, 'Rückkehr' is more natural.

Die Heimreise dauerte wegen des starken Verkehrs fast acht Stunden.
Because of the heavy traffic, the journey home took almost eight hours.
Nach ihrer Rückkehr aus Spanien erzählt Lena viel von der Reise.
After her return from Spain, Lena talks a lot about the trip.