Why one example is 2 dimension, not one dimension?

In the assignment

3.2 Dense class

Exercise

The description says:

The number of rows in the weight matrix should equal the number of columns in the variable x. Since x may have 2 dimensions if it represents a single training example (row, col), or three dimensions (batch_size, row, col), get the last dimension from the tuple that holds the dimensions of x.

Why a single training example is two dimension, but not a one dimension? (a vector?)

You always batch your dataset before passing it to the model even if it contains a single training example [N, m]. The first dimension (N) will be the batch dimension and the second dimension (m) will be the dimensionality of the vector in the case of a single training example.