Distinguishing user input numbers and characters
Variables in java are camelCase, it's odd that you follow it in cases like strName but  ignore it with MarkTotal or totalaverage. No matter what style you choose, be consistent about it, for instance I like here how the latter variable has an equals sign between it and the 0, yet everything's together in the proceeding line. Try to maintain a space between your variables, and declare only 1 variable per line. Additionally, make it a habit to define variables near where they're actually used. Narrow your scope as much as possible as it will help in future maintainability. 

These may seem like nitpicks for now, but down the line and as your programs grow they will make things easier to locate, read, and understand.

You don't need to repeatedly call System.out.println, you can use \n to add a new line where necessary. Your several calls in the beginning can be something like this:

This line:


 Marktotal= Marktotal + Mark;



Can be shortened to MarkTotal += Mark; but minding the tips I said earlier it would be more markSum += mark;

Lastly you have some variables that are only used once, when that's the case you can usually get rid of them and simply replace them with the method call.

Here's your implementation with these suggestions:

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class ForNing {
    public static void main(String args[]) throws IOException {
        BufferedReader input = new BufferedReader(
            new InputStreamReader(System.in)
        );

        System.out.print(
            "This program will calculate an individual's personal average" +
            " and then calculate the class average when instructed. " +
            "\nEnter a name: "
        );

        String studentName = input.readLine();
        int studentCount = 0;
        double classAverage = 0;

        while (!studentName.equals("finish")){
            System.out.println(
                "The follwing will calculate the average five marks of "+
                studentName +".\nPlease enter 5 marks."
            );

            studentCount++;

            int markSum = 0;
            for (int i = 1; i &lt;= 5; i++) {
                markSum += Integer.parseInt(input.readLine());      
            }

            double average = markSum / 5;
            markSum = 0;
            classAverage += average;

            System.out.println(
                studentName + "'s average is: " + average + 
                ".\n\nPlease enter the next student's name " +
                "or enter 'finish' to calculate the class average."
            );

            studentName = input.readLine();
        }

        classAverage /= studentCount;

        System.out.println(
            "The class average of all input grades is: " + classAverage +
            ".\n\nThank you for using the program."
        );
    }
}