On p. 221 of http://topology.auburn.edu/tp/reprints/v08/tp08113.pdf, I found the following definition:

"A curve is said to be *cyclic* if its first Čech cohomology group with integer coefficients does not vanish".

Here, a curve means a homogeneous metric continuum of dimension 1.

Can someone explain this definition in different, more elementary, terms, and give some examples to illustrate the meaning?