Growth mindset is a way of looking at learning and achievement originally put forth by psychologist Carol Dweck. She identified two different ways that children had of viewing their abilities. Many children have a 'fixed mindset', believing that their abilities are fairly inflexible: "I'm no good at math"; "I'm good at science". Other children had a more flexible view of their abilities: "I'm not very good at math yet"; "I've become very good at science".
The children with a fixed mindset tend to avoid situations in which they might fail. If they believed that they were poor at math, they would avoid math problems and give up more quickly when faced with math problems. Children with growth mindsets would view errors as a normal part of learning, and would be more likely to attempt difficult problems and to continue working until they solved problems correctly.
In Western culture, we have a tendency towards the fixed mindset -- we try to avoid things that we can't do well, and try to do more of the things that we think we are good at. Some studies have found that the language we use with children influences this; praise such as "you're very smart" and "you're good at this" encourage a fixed mindset, while praise such as "you're working very hard" and "I like how you keep trying" encourage a growth mindset.
Research is still ongoing into what ages and groups benefit most from a change to a growth mindset, and it is uncertain if the benefit is as clear as some proponents claim -- however, it does seem to be true that encouraging a growth mindset is never harmful, and is often helpful, so it is more and more being taught in educational settings.