Denote the $n+k$-th homotopy group of $S^n$ by $\pi_{n+k}(S^n)$ and the group of framed cobordism classes by $\Omega_n^{fr}(S^k)$. A central problem of algebraic topology is to compute $\pi_i(S^j)$ for all $i,j$. Pontryagin established that $\Omega_n^{fr}$ and $\pi_{n+k}(S^n)$ are isomorphic. Assuming that $\Omega_n^{fr}(S^k)$ are easier to compute than $\pi_{n+k}(S^n)$ this is a big leap of progress.
But then on Wikipedia (here) I found:
In more recent work the argument is usually reversed, with cobordism groups computed in terms of homotopy groups (Scorpan 2005).
Which raises the following question: which of the two is easier to calculate? Or are both difficult depending on $n$ and $k$?