Measurement in the computational basis
Suppose a Qubit is in the state $\alpha|0\rangle+\beta|1\rangle$. When you measure this qubit in the computational basis it gives you a classical Bit of information: it gives you the outcome $0$ with probability $|\alpha|^2$, and the outcome $1$ with probability $|\beta|^2$. The corresponding state of the qubit after the measurement is $|0\rangle$ or $|1\rangle$. 1
The act of measurement changes the state of the qubit as well. After the measurement, $\alpha$ and $\beta$ are gone/discarded. We have no way of knowing their values.
Measurement is denoted by an elongated semi-circle in a circuit diagram. Here, the $m$ is a classical bit, denoting either $0$ or $1$. The double wire is used to indicate the classical bit $m$ going off and being used to do something else.