Some great answers, but none of them ELI5, so I'll have a go.
When electricity passes through a non-metal, it's like trying to push a person through a wall, the person just bounces off. When electricity passes through a metal, it's like you put lots and lots of doors in the wall, so the people (electricity) can pass through it easily. Different metals have different conductivity (more or less doors).
Superconductivity is like taking the wall away completely, 100% of the people can freely pass the threshold. But, so far, we've only been able to make superconductors that work at very, very, very low temperatures; or very, very, very high pressures. Of course, it's not viable for our computer or electric cables to be cooled that much, or pressured that much.
In our modern world, with so many devices running on electricity, we lose lots and lots of energy & money to resistance (those pesky walls with not enough doors). If we had a superconductive material that works at room temperature, and normal pressure, it would mean we can send electricity around the world with very small amounts lost to resistance; it would mean our devices would become incredibly efficient; and likely lead to the development of incredible new technology.