der Birnbaum
pear tree
A fruit tree from the genus of pome fruit plants on which pears grow.
Im Frühling blüht der alte Birnbaum im Garten wunderschön weiß.
In spring, the old pear tree in the garden blooms beautifully white.

pear tree
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pear tree
A fruit tree from the genus of pome fruit plants on which pears grow.
Im Frühling blüht der alte Birnbaum im Garten wunderschön weiß.
In spring, the old pear tree in the garden blooms beautifully white.

This word is a simple compound made up of the fruit 'die Birne' (the pear) and the word 'der Baum' (the tree). So it literally describes a tree on which pears grow.
Unser Nachbar hat einen alten Birnbaum im Garten gefällt.
Our neighbor cut down an old pear tree in the garden.
The pattern 'fruit + tree' is used for many fruit trees in German. If you know the name of a fruit, you can often form the name of the corresponding tree.
Ein Apfel wächst am Apfelbaum, eine Kirsche am Kirschbaum.
An apple grows on an apple tree; a cherry grows on a cherry tree.
In connection with fruit trees like the Birnbaum (pear tree), the verbs 'pflanzen' (to plant), 'blühen' (to bloom), 'ernten' (to harvest), and 'schneiden' (to prune/cut) are often used.
Wir müssen den Birnbaum im Herbst schneiden, damit er nächstes Jahr viele Früchte trägt.
We have to prune the pear tree in the fall so that it bears a lot of fruit next year.
fruit tree
'Obstbaum' and 'Birnbaum' are closely related. An 'Obstbaum' is the general term for a tree that bears edible fruit. A 'Birnbaum' is a specific type of fruit tree, namely a tree with pears. If the exact fruit is not important or you mean different trees, you say 'Obstbaum'. If it is specifically about pears, 'Birnbaum' is more precise.

Meine Nachbarin pflanzt einen Birnbaum neben die Garage.
My neighbor is planting a pear tree next to the garage.
Im Garten steht ein alter Obstbaum, der jedes Jahr viele Früchte trägt.
There is an old fruit tree in the garden that bears a lot of fruit every year.