Specimen plants are plants grown by themselves in a lawn or garden for ornamental effect, rather than being massed with others as are bedding plants or edging plants. Specimen plants can thus serve as focal points in landscape design.
It's easy to remember what "specimen" plants are if you learn the Latin root the word is based upon. The Latin root, spec- means "to look at." Consequently, a specimen plant is one you would single out in your landscape as being particularly noteworthy, deserving of "center stage" in your yard. Most often this will be a tree, but it could also be a shrub if the latter is sufficiently large and showy.
An example of a specimen plant is a flowering tree that has a prominent spot reserved for it on a lawn. What type of tree should you use? Well, that's a highly personal choice. For example, if you have a favorite color, you might make your selection from a number of candidates whose flowers sport that particular color. But it could be any attribute that you, yourself attach value to.
I happen to use a golden chain tree in this manner in my own yard. I value the look of its abundant and long flower racemes. But again, it's a matter of personal choice. A possible objection here is that golden chain trees don't bloom long enough to warrant usage as specimen plants. My own opinion is that their brilliance while in bloom trumps the brevity of the blooming period.
Some people would make pleasing plant form the criterion they use for selecting a specimen plant, rather than pretty flowers. Their argument is that an interesting branching structure, for example, can be appreciated year-round, rather than for just the short period during which a tree or shrub blooms. It's easier to make that case in the context of landscaping for small spaces, where space constraints may limit you to one specimen plant.
Plants with interesting forms include:
Ideally (and if your landscape is large enough), you would include at least one plant you regard as a specimen plant in your landscaping for each of the four seasons. That way, you have something to look forward to throughout the year.