In an absorbing Markov chain, transient states are those states that the process may visit temporarily but will eventually leave, never to return. They play a crucial role in determining the behavior of the chain before it reaches an absorbing state. Specifically, transient states help in analyzing the expected number of steps taken before absorption and the likelihood of transitioning to specific absorbing states. By examining the transition probabilities from transient to absorbing states, one can compute metrics like the expected time spent in transient states and the probabilities of ending in each absorbing state, providing a deeper understanding of the chain's dynamics and long-term outcomes.