a loose, long-sleeved, collarless pullover of soft, absorbent fabric, as cotton jersey, with close-fitting or elastic cuffs and sometimes a drawstring at the waist, commonly worn during athletic activity for warmth or to induce sweating.
Also, sweat shirt.

1920–25; sweat + shirt

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World English Dictionary
sweatshirt (ˈswɛtˌʃɜːt)
a long-sleeved knitted cotton sweater worn by athletes, etc

Collins English Dictionary - Complete & Unabridged 10th Edition
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Example sentences
The presenter, in a bright red sweatshirt, is demonstrating how to construct a
  cardboard cut-out bumblebee.
Also included a dark colored heavy cotton hooded sweatshirt and a pair of sweat
  pants and a navy watch cap for cold nights.
Slip this sweatshirt over anything for the ultimate in relaxation whether
  you're on the bay or in the bleachers.
She was wearing a flowery rose-colored skirt, a bright blue sweatshirt, and a
  bandanna tied under her chin.
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