You can read his biography elsewhere in full, but let me say that he won the Fields Medal for some work he did on knot theory, specifically "for his discovery of an unexpected link between the mathematical study of knots and statistical mechanics".

That work is seminal, and it - to summarize - helps us count knots (technically treat topologies as polynomials). That itself is important in studies in low-dimensional topology, which can be instrumental in string theory and stuff that I do, like protein folding. When you hear others (myself included) reference the famous quote from Isaac Newton about sitting "on the shoulders of giants", Jones was somebody mathematicians and physicists alike are talking about.