You need to know: Matrix multiplication, invertible matrix, group, subgroup, group isomorphism, field, braid group.
Background: General linear group of degree n over field F, denoted as GL(n, F), is the set of 
The Theorem: On 11th March 2000 Daan Krammer submitted to Annals of Mathematics a paper in which he proved that all braid groups are linear.
Short context: In 1935, Burau suggested a way to represent elements of any braid group (braids) as matrices over some field. However, he did not prove whether it is faithful (that is, whether different braids corresponds to different matrices). In 1991, Moody showed that this not always the case. The Theorem proves that a different representation, suggested by Krammer in 1999, is faithful, thus establishing that all braid groups are linear. In May 2000, the same result was proved independently by Bigelow.
Links: Free arxiv version of the Bigelow’s paper is here, journal version of Krammer’s paper is here. See also Section 2.2 of this book for an accessible description of the Theorem.
Theorems of the 21st century 