Logic functions in C-Bus output units allow you to control output channels a bit more intelligently. Without logic you can have every channel linked to its own group or multiple channels linked to a single group, but there is no way you can have single channel linked to multiple groups.
Using logic you can make single channel "listen" to states of two or more groups. For example, you may have a requirement to program 2 channels and 2 single key units to operate on lights in conference hall and its entrance. So you could have
Channel 1 = "Conference Hall Entrance lights"
Channel 2 = "Conference Hall lights"
Key 1 = "Conference Hall Entrance lights"
Key 2 = "Conference Hall lights"
Both lights operate independently in this set-up. Now imagine you had a rule in that requirement "make entrance lights be on, when conference hall lights are on". To implement this you go to Logic tab of the Relay unit, tick one checkbox for Channel 1, select the logic group against it to be "Conference Hall lights" and set the logic function to OR.
OR logic function emulates switches in parallel. This means that the light will be ON if at least one switch is ON. ALL the switches must be OFF to turn the load off.
If you had 4 channels serving conference hall lights (i.e. Hall Centre lights, Hall Podium lights, etc), you would then need to use all 4 logic groups to implement that rule.
AND logic functions means that a channel will be on only when all groups participating in logic operation are on. Basically it emulates series connection of switches, so another way to think of AND logic is to think of a series of switches in a row with a light bulb hanging off the end (assume the supply and neutral).
The above example is for Relay output unit. There is a small difference in how logic functions work in Dimmer unit. If Max (which is OR or "greater of") is selected, then the channel level is set to the level highest in groups participating in logic operation.
If Min (which is AND or in other words "lesser of") is selected in Dimmer, then the channel level is set to the level lowest among levels in groups participating in logic operation.
If you are just turning Dimmer channels ON and OFF then Dimmer logic is the same as for relays with MIN logic giving you the equivalent of AND - and MAX logic giving you the equivalent of OR.
If you are not familiar with the basic logical functions, you can read some theory here: Basic Logical Functions and Gates