Nature of analog channels on digital/mixed oscilloscopes
Analogue channels
For sampling analogue waveforms, even digital waveforms if you want. The signal is passed through an ADC to convert it to a quantized value which is displayed on screen
Digital Channels
These are used for logic analysis. They are not passed through an ADC (well they may be but anyway), but are rather fed through an analogue comparator with some reference level producing a low or a high. These are then plotted on screen.
Why Both?
Analogue channels are expensive, especially if they are high sampling rate. You need an ADC with enough bandwidth and then the raw processing power to display the signals. However they are also very useful as you can see the full signal as a representation of voltage vs time. You can even do math functions like FFT.
Digital channels are cheap. Analogue comparator hardware is easy to implement, and because they are only 1 bit (high or low), the processing power required is much less. However you can't see what the signal looks like, just whether it is above or below a threshold. Even still, they are very useful for analyzing something like a 16 channel data bus. For example a 16 analogue channel scope would be hellishly expensive compared to one with 16 digital channels, and if you are only interested in the digital value of a signal, not what the voltage waveform looks like, then digital channels are a much simpler way of measuring it.