A locally ringed space is a ringed space such that every stalk is a local ring. A morphism of locally ringed spaces consists of a continuous map and a compatible map of sheaves that induces local homomorphisms on stalks.
Every scheme is a locally ringed space. Its sheaf of rings is its structure sheaf.
More things to try:
Weisstein, Eric W. "Locally Ringed Space." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LocallyRingedSpace.html
such that every stalk 
is a local
ring. A morphism of locally ringed spaces consists of a continuous
map and a compatible map of sheaves that induces local homomorphisms on stalks.
