Latency is fundamentally the duration of a process, and can be quantified as the difference between the time at which the process starts and the time at which it ends. Causality is essential to the concept of latency: the difference between two arbitrary unrelated timestamps is completely meaningless, and the value of defining and measuring latency arises because it captures the causality inherent in a process. In HFT, the processes of interest are primarily trading processes - for example, the process of a trader reacting to an update to the price of a traded instrument by placing an order to trade at the new price.
Latency is often undesirable, and especially so in HFT where speed and responsiveness are essential elements of the trading business. Latency bears most directly on HFT when it is a competitive factor: if two or more traders are poised to take advantage of the same price updates, then the publication of such an advantageous price update signals the start of a race among those traders. The one with the lowest latency will be the first to get their order back into the market to lift the liquidity available at that price; those with higher latency are likely to be unsuccessful in their attempts.