The notation in which all our numbers are written is called the place value notation. You may have had exercises in class 5 and 6, maybe, concerning decimal expansions of the a number. For example, $678 = 6 * 100 + 7 * 10 + 8 * 1$, and $1089 = 1 * 1000 + 8 * 100 + 9 * 1$.
Therefore, using elementary algebra, we can deduce that given a three digit number represented by $abc$ is the number $100a+10b+c$. Here, I say represented by because in ordinary algebra $abc$ is the product of the three quantities a,b, and c, but here we are treating it as the representation of a three digit number e.g. $678$.
From the representation $abc$, we deduce that $a,b,c$ stand for the digits of the number. For example, when we write $678$, then the digits of the number are $6,7,8$.
Now, we are in a position to actually understand the problem at least : it says which is the largest three digit number is $37$ times the sum of it's digits?
Let this number be $abc$. Note that this is a representation. The actual number, of course, is $100a+10b+c$, and this is equal to $37$ times the sum of digits which are $a,b,c$, hence giving the equation $100a+10b+c = 37a+37b+37c$.
When it comes to solving this question, you should realize that our three digit number is at least a multiple of $37$, the quotient being $a+b+c$. So it's enough to check multiples of $37$. Furthermore, since we have to find the largest such number, we may as well start from the largest three digit number possible, which is $999$. This in fact satisfies all the requirements, but doesn't have distinct digits.
So we come further down by subtracting $37$. The next number is $962$, doesn't work. The next is $925$, doesn't work. The next is $888$, doesn't have distinct digits, ... (once you understand why we are doing all this, I can tell you ways of reducing the number of cases to check in this step, because it's time intensive).
Work your way down, until you find the right answer, which I think is $37*17 = 629$. The sum of the digits is $17$, indeed, and the digits are distinct.