Baseband vs Bandpass Signal
Starting with a Bandpass signal - this is a signal that has a bandwidth $BW$ about a center frequency $f_c$, so the signal content goes from $f_c-1/2BW$ to $f_c+1/2BW$. For a real signal (i.e. not complex) the their is also the corresponding negative frequency component i.e. the signal also exists at $-f_c$.

Basebanding often refers to shifting this signal down to DC. This is done by mixing the signal (modulating) it with $\exp(-j2\pi f_c t)$ and low pass filtering to remove the component that was originally at $-f_c$ and gets moved to $-2f_c$ due to the shifting. The component that was at $f_c$ and gets moved to DC is kept by the low pass filter. This signal is now complex due to the loss of conjugate symmetry. This resulting signal is referred to as the Baseband signal.

Note that the mixing signal $\exp(-j2\pi f_c t) = \cos(j2\pi f_c t)-j\sin(j2\pi f_c t)$, which is often how you see it implemented in communication systems.

You can achieve the same result by using the Hilbert transform which essentially removes the negative frequency component and then shifts the signal down to baseband.

References:
Haykin - Communication Systems (but almost any communications textbook), also Crochiere - Multirate Digital Signal Processing (somewhere in the first couple of chapters they explain this).