Black spider with a white spot on its back
The spider in your photos is the bold jumping spider or daring jumping spider, scientifica name: Phidippus audax in the family Salticidae. As their name implies, jumping spiders are active hunters who can leap several inches to leap across gaps or pounce on their insect prey. They also have one pair of their eight eyes greatly enlarged, giving them excellent forward vision. They see movement very well, and will seemingly turn to follow the motion of anything moving near them, be it insect prey or your finger. These spiders normally live outdoors, but can also occasionally be found indoors, especially the males who wander considerably looking for females. These spiders are harmless, and some people even keep them as pets. I have included some links below to websites with more information about these spiders.