This pretty purple plant is called Purple Heart, Purple Queen, or Wandering Jew. There are several kinds of Wandering Jew plants, Tradescantia genus, and this plant is specifically called Purple Heart (or Purple Queen): Tradescantia pallida.
This plant is native to Eastern Mexico and do really well in frost-free climate. Those pretty flowers are actually invasive plants. To be put in garden, the plant requires lot of maintenance to control the plant without having it taking over entire garden. This is partially reason why this plant is better off as household plant, or planted in the pot instead in the garden.
But do be careful when having this plant in the house with pets. Purple Heart is toxic to dogs and cats and can cause allergic dermatitis (rash).
My iNaturalist observation can be found here.