A nursery, or 'nurseries' in plural, typically refers to a shop which sells gardening supplies. It is sometimes referred to as a plant nursery. It may also refer to a baby's room but this is not the context we are referring to here.
A nursery is actually a good word to describe a centre which sells plants. Nursery is a word which means to 'nurse' or 'nuture'. A plant nursery is a place where plants are nurtured, propagated and grown to a desired age. Once the plants have grown to a desired size or age, they are sold to the general public or direct to businesses.
Not all nurseries are the same. There are some nurseries that specialise in certain phases of plant growth. Some nurseries may specialise in only propagation, growing out, retail sale, or may only sell one kind of plant species only. You may also find that nurseries may sell different kinds of plants depending on which area of the world they are in, and which season they are in, as this may affect which plants will thrive.
Many nurseries sell to the general public, but not all nurseries will as this may not be the purpose of their business or organisation. There are some nurseries that are focused on the growth of trees for forestry or conservation biology. There are also some nurseries whose sole purpose is for research for feilds such as agriculture or climate change.
A great place to go to find information on nurseries in your local area are websites such as Local Business Guide. Word of mouth also goes a long way!