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What exactly are tensors?

I recently started working with TensorFlow and I read that it turn's data into tensors.I looked it up a bit but I'm not really getting it, Would love an explanation.
gpt
The word "tensor" is overloaded in mathematics, statistics, and computer science. In this context (TensorFlow, and data science more generally), tensor usually just refers to an array of numbers (which may be higher dimensional than a vector or a matrix, which are 1- and 2-tensors, respectively). This is similar to the way that "vector" is often used to mean "a list of numbers", even though the word has a more technical meaning in mathematics.

The mathematical meaning is more complex, and is a bit hard to motivate if you're not already working in a field that would have use for them. A high level conceptual view would be that a tensor is a function that eats vectors and spits out a number. These generally arise in situations where you have a space, along with some kind of geometric structure, and the tensors themselves encode some kind of geometric information about the space at each point -- that is, at any point you have a bunch of vectors (which may describe e.g. the dynamics of an object, or some other kind of information), and the tensor takes those vectors and spits out a value quantifying some feature of the space. 

One very common example is given by objects called Riemannian manifolds, which are essentially spaces which locally look similar to Euclidean space, but globally might have a very different structure. At each point, these spaces can be "linearized" to look like the vector space Rn, and they come equipped with a dot product that takes two vectors and spits out a number. This dot product in some sense defines the local geometry of the space, since it determines when two vectors are orthogonal, and allows us to define things like the length of a vectors and the angle between two vectors. This "thing" is called the metric tensor.