Once the prompt is a sequence of tokens, each token is converted into a list of numbers that places it at a point in a space with many dimensions. You can think of this space as a map of meaning: two tokens that are used in similar contexts end up near each other, and tokens used in unrelated ways end up far apart.
A useful way to picture it is a two-dimensional map where one axis roughly separates living things from objects and another separates things that move from things that stay still. On such a map, "cat" and "dog" would sit close together, "cat" and "bicycle" would sit farther apart, and "skateboard" would land near other rideable objects. Real models use hundreds or thousands of dimensions rather than two, so no single axis means anything as clean as "alive" or "moving". The directions are learned from data and are not individually interpretable. What matters is the geometry: distance reflects similarity of use, and direction can encode relationships, so the step from "king" to "queen" resembles the step from "man" to "woman".
This is the bridge from text to conditioning. Because meaning is a position, a prompt is not a string of symbols to the model but a shape traced through meaning space. Words that pull in the same direction reinforce each other; words that pull in opposite directions create tension the model has to resolve.