To my knowledge a free Google account gets 15 GB of storage by default. Somehow I now have 115 GB. How did this happen and how long do I have it for? I know smartphone sometimes prompts me to take pictures of an area I am in. Is this the result of some sort of rewards program?
Yes. Google is promoting the Local Guides feature on its Maps application:
Google Drive storage promotion
Local Guides who reach Level 4 by 11 p.m. EST on 17 March 2017 can unlock 100 GB of free Google Drive storage. The benefit must be redeemed within 30 days of issue and is valid for one year. This promotion will expire after the cut-off date.
Apparently, you sent enough pictures and shared enough knowledge with the Maps network to qualify for the reward.
If you go to https://www.google.com/settings/storage and click "view details" under the pie chart, it'll show you exactly where your storage allotment is coming from.
If you recently bought a new phone/device chances are the manufacturer has a deal with Google, and that could be how you got it...