This is indeed a beautiful peony, and it looks very healthy.  There are 4 types of peonies:  1.  Woodland peony, a separate species of herbaceous peony that prefers shade.  They are low-growing (1-1.5 feet tall), self seed and produce blue and red seed pods in the fall.  2.  Tree peony grows to from 20 inches to 8 feet tall.  They are deciduous, but the stems overwinter like a tree trunk.  They can produce dinner-plate sized flowers.  3.  Herbaceous peony, best known type of peony.  Long-lived (50-70 years) they come in an amazing range of forms and colors. individual blooms last 7-10 days.  4.  Intersectional (itoh), a hybrid of herbaceous and tree peonies.  They have large blooms (like the tree peony parent) but short stems and grow to about 2.5 feet tall by 3 feet wide.  They are more disease resistant than herbaceous peonies. 

There are 4 flower forms in herbaceous peonies.  1.  Single - like your peony, have a single layer of petals surrounding a center of pollen-bearing stamens.  2.  semi-double - broad petals intermingle with petal-like stamens.  3.  double - dense centers look like petals, but are transformed stamens.  4.  anemone form - often included in the semi-double form, have more than one row of guard petals surrounding thin petal-like stamens. 

All peonies require a cool period to bloom (like bulbs), and they  bloom in the spring.   Except for woodland peonies, most peonies like full sun, fertile, well-drained soil with lots of organic matter and moderate moisture during our dry summers.  To encourage flowering place the plant in a northern exposure with no mulch in winter (mulch after they've finished blooming in spring).  Light fertilization with bulb fertilizer (low nitrogen) should be applied when the plants reemerge in the spring, and again in the fall when the plants die back.   Tubers should be planted so the eyes are about 2 inches under the soil.  This article gives more information including about peony diseases, Peony Types  http://www.ladybug.uconn.edu/FactSheets/peonies.php.