What is a tensor?

Well, I don't blame you. For instance, here is a technical definition of a "tensor", if you can understand it. Good luck to you.

An nth-rank tensor in m-dimensional space is a mathematical object that has n indices and m^n components and obeys certain transformation rules. Each index of a tensor ranges over the number of dimensions of space. However, the dimension of the space is largely irrelevant in most tensor equations (with the notable exception of the contracted Kronecker delta). Tensors are generalizations of scalars (that have no indices), vectors (that have exactly one index), and matrices (that have exactly two indices) to an arbitrary number of indices.
Tensors provide a natural and concise mathematical framework for formulating and solving problems in areas of physics such as elasticity, fluid mechanics, and general relativity.
The notation for a tensor is similar to that of a matrix (i.e., A = (a_(ij))), except that a tensor a_(ijk...), a^(ijk...), a_i ^(jk) ..., etc., may have an arbitrary number of indices. In addition, a tensor with rank r + s may be of mixed type (r, s), consisting of r so-called "contravariant" (upper) indices and s "covariant" (lower) indices. Note that the positions of the slots in which contravariant and covariant indices are placed are significant so, for example, a_μν ^λ is distinct from a_μ ^νλ.
While the distinction between covariant and contravariant indices must be made for general tensors, the two are equivalent for tensors in three-dimensional Euclidean space, and such tensors are known as Cartesian tensors.