How do Markov Chains work and what is memorylessness?

Question

How do Markov Chains work? I have read wikipedia for Markov Chain, But the thing I don't get is memorylessness. Memorylessness states that:

The next state depends only on the current state and not on the sequence of events that preceded it.

If Markov Chain has this kind of property, then what is the use of chain in markov model?
Explain this property.

Answer 1

You can visualize Markov chains like a frog hopping from lily pad to lily pad on a pond. The frog does not remember which lily pad(s) it has previously visited. It also has a given probability for leaping from lily pad Ai to lily pad Aj, for all possible combinations of i and j. The Markov chain allows you to calculate the probability of the frog being on a certain lily pad at any given moment.

If the frog was a vegetarian and nibbled on the lily pad each time it landed on it, then the probability of it landing on lily pad Ai from lily pad Aj would also depend on how many times Ai was visited previously. Then, you would not be able to use a Markov chain to model the behavior and thus predict the location of the frog.