Baud rate is the number of symbols per second. Bit rate is the number of the information bits per second.
To see the difference, consider a transmission line capable of having 4 different states, say
3V. And the end equipment is able to detect each one of them. In this case each symbol would be one of these four states. And each symbol will carry two bits of information as opposed to the simple binary (2-state) line carrying a single bit at a time. Now consider both, the 4-state line and the 2-state line are capable to switch the states in the same rate, which is making both of them to have the same baud rate. But the 4-state line will transmit twice as many bits as the 2-state one, having the bit-rate higher two times.