Depressions:
Depressions are low pressure areas which are caused when air rises
The air rises because it is warmer than air around it or it can be forced up by high land
As the air rises it cools and clouds form
This causes unsettled changeable weather
Depressions are often associated with fronts
A front is where hot air is next to cold air
The warm air is forced upwards, it cools and condenses causing clouds and rain

Anticyclones:
Anticyclones are much the opposite of depressions
Anticyclones are associated with high pressure which is caused by sinking air
They bring settled / good weather
Because air is sinking, air is not able to rise from below so no clouds or rain are able to form
Anticyclones do bring fog and mist which in cold weather can lead to bad road conditions