Theory:

The Tamarind gives us pleasant shade,
The Date’s leaf is as sharp as a blade,
The Teak tree gives us useful wood,
The Mango gives us fruit that is good.
Explanation:
 
The tamarind tree is a huge tree that produces tamarind, an edible fruit with a sour and sweet taste. It is one of the primary ingredients in Indian cooking, and the tamarind is found within a shell. It gives a cool, enjoyable shade during hot summers.
 
tamarind-tree.jpg
Tamarind tree with tamarind in shells.
 
The date palms are tall trees, similar to coconut trees. They don't provide shade like peepul, banyan or neem trees - but the date fruits are tasty, healthy and full of nutrients. The leaves are long and sharp. The poet says the leaves are sharp as a blade, meaning that it can even cut through other objects. But it is used for poetical imagination and rhyme only.
 
palm-tree.jpg
Date palms.
 
The teak tree gives us wood that is used for making furniture. The wood from the teak tree is very strong and remains useful for hundreds of years.
 
teak.jpg
Teak wood.
 
Lastly, the poet writes about the mango tree, which gives us tasty mangoes. Mango is a sweet juicy fruit, loved by one and all. It is grown during summers.
 
mango-tree.jpg
Mango tree.
Reference:
State Council of Educational Research and Training (2019). Term-1 English Standard-6. Trees - Sara Coleridge (pp. 123-124). Published by the Tamil Nadu Textbook and Educational Services Corporation.