I am giving a presentation in two days about a search engine I have been making the past summer, and my research involved the use of singular value decompositions, or in other words, $A=U\Sigma V^T$. I took a high school course on Linear Algebra last year, but the course was not very thorough, and though I know how to find the SVD of a matrix, I don't know how to explain what I have in my hands after the matrix has been decomposed.
To someone who has taken linear algebra, I can say that I can decompose a matrix A into matrix $\Sigma$, whose diagonal holds the singular values, and matrices $U$ and $V$ whose columns represent the left and right singular vectors of matrix $A$. I am not sure how to explain what a singular value or what left/right singular vectors are. I can still be satisfied if there is no easy way to explain what this decomposition means, but I always prefer keeping the audience as informed as possible.