Connate parts are similar parts fused together. In the morning glory Ipomoea 'Heavenly Blue', petals are connate.
Connation can affect each whorl, sepals, petals, stamens, and/or carpels. When the petals are connate, at least at their base, the flower is sympetalous. (syn- or sym- means united).
Photo by K. R. Robertson at Cambridge, Massachusetts.