How to understand / imagine what is a line bundle Wikipedia says:

In mathematics, a line bundle expresses the concept of a line that
  varies from point to point of a space. For example a curve in the
  plane having a tangent line at each point determines a varying line:
  the tangent bundle is a way of organising these. More formally, in
  algebraic topology and differential topology a line bundle is defined
  as a vector bundle of rank 1. Line bundles are specified by choosing a one-dimensional vector space for each point of the space in a continuous manner.

But I do not understand it clear. I have been reading several definitions but I do not manage to understand it. Any help?
 A: A vector bundle of rank n over a manifold $M$ is a map $\pi:V\to M$ such that for each point $p\in M$ $\pi^{-1}(p)$ has a n-dimensional vector space structure. We say a vector bundle of rank n over a manifold $M$ is trivial if it is isomorphic to $M\times \mathbb{R}^n$. In fact we require that our vector bundle be locally trivial, which means that around each point in $M$ there is a neighborhood $U$ so that $\pi^{-1}(U)$ is trivial. You can think of a vector bundle as a Manifold with a vector space glued to each point. The motivating example for vector bundles is the tangent bundle, which is simply $\coprod_{p\in M} T_pM$, ie the disjoint union of the tangent space at each point, with the minimal topology and smooth structure needed to make the map which sends every element of $T_pM$ to $p$ a smooth function. 
An interesting example of a line bundle is the Mobius bundle.
 
The mobius bundle is a vector bundle over $\mathbb{S}^1$. It is a rank 1 vector bundle because you can view it as a circle with a copy of $\mathbb{R}$ at each point. Interestingly enough the mobius bundle is not orientable, so it cannot be isomorphic to the trivial bundle.
