Table Mountain National Park is huge, and the Silvermine Nature Reserve makes up part of the enormous park. The reserve takes its name from the Silvermine Reservoir, which was built in 1898, and which forms the centerpiece of the reserve. (It's not meant for swimming, but it makes for nice scenery.) Seventeenth-century Dutch settlers thought they would find silver in the area, and although they didn't, the name stuck.
The reserve is well-known for its abundant fynbos plants, indigenous plants that grow in a specific area in the Western Cape. It's a popular spot for Cape Town residents to picnic, hike, mountain bike, or simply enjoy the scenery on a nice day. There are also some interesting caves to explore at one end of the reserve.
The Silvermine Nature Reserve is open daily from 7am-7pm. Admission is SAR30 for adults and SAR15 for children ages 1-11.