Linear independence refers to a set of vectors in a vector space where no vector can be expressed as a linear combination of the others. This means that each vector adds a unique direction or dimension to the space, contributing to its overall structure. If a set of vectors is linearly independent, the only solution to the equation formed by their linear combination equaling zero is when all coefficients are zero. In contrast, if a set of vectors is linearly dependent, at least one vector can be written as a combination of the others. This indicates redundancy within the set, as some vectors do not provide new information about the space. Understanding linear independence is crucial in fields like linear algebra and machine learning, where it helps in determining the basis of vector spaces.