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A cosmic string is a line in space that is a type of discontinuity of the universe's typical near-Euclidean geometry of space-time (i.e., a type of topological defect). Theories were developed in the 1970s about cosmic strings' formation in the early universe, their explaining power regarding some observed phenomena (specifically the clumping of matter), and possible methods of detecting or verifying their existence. Alternate explanations have become more popular, apparently fitting nicely with some observations, and there has been no widely-recognized sign of their existence.
Cosmic strings are not the eponymous strings of string theory, though string theory provides some theory behind them. Cosmic strings would be defects in the geometry of space as are the singularities within black holes and (in theory) wormholes. A circle encircling a cosmic string would have less than 2π circumference. They would effectively exert gravitational force, propagating from the line. Gravitational lensing by one would create two full images, e.g., two views of the same galaxy.
A process occurring near the beginning of the universe, symmetry breaking, is considered a possible source of cosmic-string (one-dimensional) discontinuities, and also a possible source of other kinds of such discontinuities (topological defects), magnetic monopoles (zero-dimensional), domain walls (two-dimensional), and textures (three-dimensional).