These discourse markers are used to introduce the two sides of an argument.
Study the following sentences.
- On the one hand, I would like to earn more money, but on the other hand, I am not willing to work the extra hours.
- On the one hand, he wants to attain salvation, but on the other hand he is unwilling to give up the little pleasures of life.
- On the one hand, there are valid reasons to regulate the internet. On the other hand, regulating the internet by introducing stricter policies might impair its functionality.
- On the one hand, he complains about his loneliness. On the other hand, he shows little interest in socializing.
On the one hand is not usually used alone. It is almost always followed by on the other hand. On the other hand can be used alone.
- Arranged marriages are very common in many Asian countries. On the other hand, in the West they are quite unusual.
Note that discourse markers like on the one hand and on the other hand are not grammatically connected to the sentence. They can be removed and the sentences will still be grammatically correct. Of course, some meaning would be lost, but there would be no ungrammaticality.