Your plant is Pink Quill, Tillandsia cyanea. It’s an epiphyte, one of the so-called air plant.  It grows in tropical cloud forests while perched on a tree branch but may be grown in a container if potted in orchid bark or a combination of orchid bark and cactus mix.  When grown as a houseplant, it needs bright light but not direct sunlight; humidity; and room temperatures with a minimum during the winter of 59 degrees.

It’s important to know that the original plant won’t bloom again, but its new offsets – sometimes referred to as “pups” – will.  You can keep the original flower spike as long as you think it is attractive or you can remove it after it has dried. The key to rebloom Pink Quill is to provide excellent growing conditions similar to its native habitat so that it develops new offsets at its base which can bloom. In other words, mimic a cloud forest while perched on a tree branch. Some people are successful growing them on a bright window sill above the kitchen sink or in a bright bathroom.

See http://indoor-plants.net/tillandsia-cyanea/ and http://www.livingmemoriesofmaui.com/plant-care/lava-rock-tillandsia-cyanea/.

Are the brown part of the plants the offsets you were referring to? Should I pull them off the plant and set them in water to try to grow roots, or try to plant them after removing from the plant? Thanks!

Thanks for including another image with your question.

The life cycle of a bromeliad such as your Pink Quill is to flower, then die.  But before the “mother” plant dies completely, it recycles its nutrients while producing one or several fresh new plants – the offsets or “pups” – at its base.   The offsets will bloom at some future time. I suspect your biggest challenge will be to create a small piece of Hawaii here in Oregon.

The brown parts in this image may be remnants of the original plant.  They’re dead and should be removed. From the appearance of the plant, it appears you have about 3 offsets which sprouted from the original plant. They may take a while to produce their own flowers.  You don’t need to remove them but can leave them in place to eventually have a potful. See http://www.ourhouseplants.com/plants/tillandsia-cyanea-lindenii.