Vector

A vector holds $n$ numbers in a fixed order, written $v \in \mathbb{R}^{n}$. One index reaches any element. Almost everything you handle in machine learning is one: a word embedding, a row of features, a layer's bias, the gradient of a loss with respect to a parameter block.

The useful mental model is geometric — a vector is a direction with a length, which is what makes the dot product, cosine similarity, and norms meaningful operations on it rather than arbitrary arithmetic. A 768-dimensional embedding is a direction in 768-dimensional space, and "similar meaning" becomes "similar direction".