Many gardens have areas that don't get much sun during the day due to nearby buildings or things above an area. This is often called heavy/full shade, where an area might get less than around 3 hours of sun in the summer, and in these areas, plants not suited might not grow properly.
Planting in shade
Potential causes of full shade might be areas near a building, where in the UK a north facing garden with the house on the south-most side would get a lot of shade. You may also get this in areas with something above it like dense branches/leaves on a tree, where thinner branches/leaves might cause dappled shade and denser one's full shade. In some cases, if you prefer plants that need more sun, you may be able to for example trim the lowest branches to let more light through.
Soil is an important consideration in shaded areas, where it might be dry, damp, or in-between. Areas near trees for example might be dry shade, where the tree roots might use a lot of the nearby moisture. Areas near buildings might be dry/damp depending on how much rain gets to them and other nearby water sources. Both situations might also get fairly average moisture. To work out which scenario you have, see the soil at different areas in your garden after different weather conditions and maybe compare them.
Alongside plants suitable for shade, you might also try and include things nearby that make the most of the light available. You could use materials that reflect light, a pond for example, or instead focus on plants that have a lot of colour/texture to balance out the lower light in that area.
Plants to use for a shaded area
The plants you might use would depend on the look you're after, your climate and the moisture in the soil. Below we give some plants that are generally suited to shade in the UK. Keep in mind specific plant varieties may be more or less suited to full shade and may prefer certain amounts of moisture.
Cyclamen hederifolium
Cyclamen hederifolium are hardy perennial flowers. Often called ivy-leafed cyclamen, as their leaves look similar to ivy, this variety of cyclamen can grow well in partial shade, so under trees and fairly near walls, and also grow fairly well in full shade or dry shade. They're quite resistant to the cold weather you might get in the UK. They'll spread slowly when they grow well (less so in full shade vs partial shade).
Hosta
Hostas are hardy perennial flowers. There's a range of varieties, all of them are very hardy. Many varieties are shade tolerant ranging from full sun to partial/full shade, generally preferring not to get too hot in the summer. You can plant them in your garden or in a pot, and they like soil that retains a lot of water but isn't waterlogged. If planted in a pot make sure it's fairly large and has some holes for drainage.
Hydrangea petiolaris
Hydrangea anomala subsp. petiolaris are hardy evergreen shrubs. Often called climbing hydrangea, they can grow well in partial/full shade and tend to like some moisture, so are well suited for a damp shaded area. They have self-clinging roots, so you might grow them on the shaded side of a wall.