We know that the numbers that are obtained by adding consecutive numbers are called triangular numbers.
The first triangular number is $1$. The next one is $3$. Going on further, we get,

 $1+2+3=6$

$1+2+3+4=10$

$1+2+3+4+5=15$
Hence, the next triangular number after $10$ is $15$ i.e the correct answer is option B.