die Brust
chest
The upper front part of the human body between the neck and the abdomen; the rib cage.
Beim Atmen heben und senken sich Brust und Bauch.
When breathing, the chest and abdomen rise and fall.

chest / breast
Loading your saved state.
chest
The upper front part of the human body between the neck and the abdomen; the rib cage.
Beim Atmen heben und senken sich Brust und Bauch.
When breathing, the chest and abdomen rise and fall.

The meaning of 'Brust' (chest / breast) becomes clear from the context. In a medical context or with 'atmen' (to breathe), it refers to the chest/rib cage. In connection with 'Baby' (baby) or 'stillen' (to breastfeed), it refers to the female breast. In recipes or cooking, it refers to poultry meat.
Er hat seit gestern Schmerzen in der linken Brust.
He has had pain in his left chest since yesterday.
When 'Brust' (breast) refers to food, it almost always appears in a compound word. This lets you recognize the meaning immediately. Typical examples are 'Hähnchenbrust' (chicken breast), 'Putenbrust' (turkey breast), or 'Entenbrust' (duck breast).
Im Supermarkt kaufe ich oft geräucherte Putenbrust für das Frühstück.
At the supermarket, I often buy smoked turkey breast for breakfast.
The idiom 'sich in die Brust werfen' (to puff oneself up) is reflexive and means to present oneself proudly or arrogantly. The structure is fixed: the subject throws 'sich' (oneself; accusative) into the chest.
Nach seinem Sieg warf sich der Athlet vor dem Publikum in die Brust.
After his victory, the athlete puffed himself up in front of the audience.
The phrase 'aus voller Brust' (at the top of one's lungs) is a fixed expression meaning that someone sings, laughs, or shouts very loudly and with a lot of energy. It functions like an adverb.
Die Fans im Stadion sangen aus voller Brust die Hymne ihres Vereins.
The fans in the stadium sang their club's anthem at the top of their lungs.
In a medical context, 'Brust' (chest) is often connected with 'Schmerzen in der Brust' (chest pain) or 'einem Druck auf der Brust' (pressure on the chest). These phrases describe typical symptoms.
Bei einem Druck auf der Brust sollten Sie einen Arzt aufsuchen.
If you feel pressure on your chest, you should see a doctor.
back
'der Rücken' and 'die Brust' are both parts of the upper body, but they are on opposite sides. 'der Rücken' is at the back of the body; 'die Brust' is at the front between the neck and the abdomen. You can confuse them when describing body parts or talking about pain. The important thing is the direction: the back is 'der Rücken', the front is 'die Brust'.

Nach dem schnellen Lauf spürt sie ein Stechen in der Brust.
After the fast run, she feels a sharp pain in her chest.
Beim Tragen des Rucksacks spannt Frau Krüger den Rücken an.
While carrying the backpack, Ms. Krüger tightens her back muscles.