spare umbrella kept at work or school
An umbrella left at a workplace or school in case of unexpected rain, so one doesn't have to carry it daily.
I keep a spare umbrella at the office, so I'm not worried about sudden rain.
Many students keep a spare umbrella in their school lockers.
Compound of 置き (oki, 'placing') + 傘 (kasa, 'umbrella'). The exact historical derivation is uncertain, but the word transparently means 'an umbrella that is placed/left'.