Suppose Alice wants to send encryptions (under a one-time pad) of $m_1$ and $m_2$ to Bob over a public channel. Alice and Bob have a shared key $k$; however, both messages are the same length as the key $k$. Since Alice is extraordinary lazy (and doesn't know about stream ciphers), she decides to just reuse the key.
Alice sends ciphertexts $c_1 = m_1 \oplus k$ and $c_2 = m_2 \oplus k$ to Bob through a public channel. Unfortunately, Eve intercepts both of these ciphertexts and calculates $c_1 \oplus c_2 = m_1 \oplus m_2$.
What can Eve do with $m_1 \oplus m_2$?
Intuitively, it makes sense that Alice and Bob would not want $m_1 \oplus m_2$ to fall into Eve's hands, but how exactly should Eve continue with her attack?