You have to look at it as a sequence of time steps which can interact. You can implement this interaction in many ways, such as transformer, mamba, rwkv or mlp-mixer. But the purpose is always to allow communication across time.
You use three distinct linear projections, one for queries, one for keys and one for values. From Q and K you compute the attention matrix A, and using A you construct linear combinations from V. But depending on A, for example for a token V_i there might be input from two other tokens, V_j or V_k, so information is moved between the tokens.