The Piggyback plant is happy indoors or out; the Royal Horticultural Society lists it as being hardy to -20c. It isn’t a fan of direct sun, and hates drying out, so it is best planted or grown in shade.
Native to the west coast of the US & Canada, it has naturalised in the damper parts of the UK. Its handful of a name comes from being named after both Mr. Tolmie and Mr. Menzies; the common name refers to its unusual reproductive habits. It has many other names: child-on-your-lap, youth-on-age, mother of thousands.
While the plant flowers and produces seed, it also developes mini-plants on top of its leaves. To grow a new plant from one of these, you just need to pick both the old and new leaves off the plant and put them face-up, on a tray or pot of compost. Hold the old leaf down with a pebble or paper clip so it stays in contact with the compost and in a few weeks it will root and make a new plant.
Indoors you can grow it as a hanging plant if you leave the plantlets on, it will gradually form an upside down teardrop shape with the added bonus of small sprays of delicate burgundy flowers. Outside it is good for the front of a border, containers and baskets. There is a splotchy, yellow variegated version and a plain green one.
HomePlants 
This is naturalised in my front garden in Sussex where I released it about 10 years ago after keeping it as a houseplant for a few years. It lives happily in dappled shade amongst cotinus, which colour co-ordinates with the flowers, and ivy.
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One of them (can’t remember if it is the variegated or non-variegated form) is from your plant!
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