Chaenomeles speciosa, or flowering quince, is in bloom these days. I passed the one below at the Liz Christy Garden, though I wish I could have run up to Conservatory Gardens to get a snapshot of the large quince hedge on the north side of the gardens. You should definitely head up there this weekend. Not only is the quince in bloom, but you can also see the beds of tulips and no doubt, a mix of late-season daffodils.
This plant does not bear the tasty fruit that makes quince jellies, that plant is Cydonia. Chaenomeles have small, bitter, apple-like fruit. However, the two genera are related, found under the umbrella of the Rosaceae family, along with - to name a few- apples, plums, pears, cherries and peaches.
Chaenomeles is one of those great heirloom-y plants, common in Victorian-era gardens. Most species are a hybrid of C. speciosa, or C. x superba (or both). There is not a wealth of modern cultivars for this plant and as a result, you may find this to be a bit of a high maintenance plant. For instance, the hedges of quince in the Conservatory Gardens are perpetually covered with aphids.
The name Chaenomeles is derivative of the Greek word for chainen, which means to split, and meles, the Greek work for apple (like Malus - the genus name for apple).