Hilbert's Basis Theorem states that if you have a Noetherian ring, then every ideal in that ring is finitely generated. This means that any ideal can be created using a finite number of elements from the ring. This theorem is significant in the field of abstract algebra because it helps to understand the structure of ideals in rings. The theorem is named after the mathematician David Hilbert, who made substantial contributions to various areas of mathematics. Hilbert's Basis Theorem is particularly important in commutative algebra and has implications in algebraic geometry, where it aids in the study of polynomial rings and their properties.