To round off a number to the nearest hundred, we have to observe the tens place.
For, $7834$ which is a $4$ digit number, the tens place value is $3$. Now, $3<5$ so $7834$ is rounded down to $7800$.
For $127$ again, the tens places value $2<5$ so we round it down to $100$.
Adding up our numbers we get an estimate of $7900$ which is pretty close to the original sum of $7834 + 127 = 7961$.