Polynomial time
Theoretical computer science
A running time bounded by some fixed power of the input size. Problems solvable this way form the class P and are treated as tractable.
What is usually left out
The identification with "efficient" is a useful convention rather than a fact. An algorithm running in n¹⁰⁰ steps is polynomial and useless, while the simplex method is exponential in the worst case and excellent in practice. The convention earns its place because the class is robust: it does not change under reasonable changes of machine model.