It's wet, the soil is waterlogged and this is when plants literally drown. As the water fills air spaces between soil particles oxygen cannot reach the roots, the soil stagnates and root growth stops. Leaves will wither and fall, puddles will form on the surface and shoots will die off. If the soil becomes compacted drainage will suffer and disease will flourish in these ideal conditions. To avoid this try not to walk on wet soil,spike lawns and add lime free sand to improve drainage, dig up waterlogged plants and remove damage roots.
Replant in pots with free draining compost. Also try to improve the soil conditions to try to prevent this happening. Apply mulch over the root area, in clay soils use plenty of organic matter and horticultural grit to improve drainage and consider installing a drainage system or soak away. Digging ditches filled with gravel will help drain water away from the garden.
The other thing that wet weather brings in abundance is pests. Slugs, earwigs, pill bugs and ants to name a few. Moisture encourages pest reproduction and growth with ants being at the forefront as they build their nests in just about any area outdoors. Snails are dormant during Autumn and Winter but are increasingly active in warm weather whereas slugs are active all year particularly after dark or in the wet.
These pests cannot be fully eradicated so the protection of vulnerable plants and seedlings is essential. Nematodes can be used to great effect, applied to the soil in the evening and other control methods include melon, orange and grapefruit skins laid cut side downer jars part filled with beer sunk into the ground. Copper tape around pots and gel repellents discourage or you can go out at night and pick them from plants and move to waste land nearby or destroy with salt.
Another way to discourage these pests is to use plants they are less likely to eat. There are more than you think with Acanthus Mollis, Poppy, Anemone, Foxglove, Salvia and Nasturtium to name just a few. Discouraging these pests also give you a good excuse to create new flower beds in your garden.