Anything that's uncontrived is natural or spontaneous, rather than fake or pre-planned. An uncontrived speech feels real and heartfelt rather than overly rehearsed and stiff.
If something is false or carefully constructed to appear a certain way, it's contrived. When you add the prefix un-, "not," you get uncontrived. It's a great way to describe things that are genuine. A photographer might prefer taking uncontrived, candid shots of passersby, rather than staging more formal studio portraits.