I saw the following question in a book.
Question: What will you do if the teacher is not in the class?
Answer : I am row leader so that's why I will mind my row.
Can you please explain the meaning of "I will mind my row"
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Mind has many meanings, one of which is:
"to look after someone, usually on a temporary basis"
The person in your example is saying that, when the teacher is not in class, they will take care of the other students in the same row to which they have been appointed as row leader. Presumably, this would require the row leader to ensure that the other students behave themselves and do whatever work the teacher has set until the teacher returns.
It most probably goes for I'll take care of those who sit in the same row as me, so that they won't misbehave and the teacher won't have to tell us off because of it. Check the definition of row in LDOCE (5th edition):
1. a line of things or people next to each other → column
2. a line of seats in a theatre or cinema
At least in British English, a minder is
a person whose job it is to look after someone or something. eg:"a baby-minder"
The Answerer in your example has a duty to make sure the people in their row of desks aren't mis-behaving, deputised from the teacher. So while the teacher is away they'll continue to look after their row.