If you are working with HMMs a good book to read is "Hidden Markov Models for Time Series An Introduction Using R". Look into the page 35 and you shall have a better understanding of this measurement. However, keep in mind that the likelihood is a cumulative product of probabilities, which leads you to problems with the decimal precision.
To avoid this, in practice, the log likelihood is used, you can see more about this in the same book.
Considering poison HMMs, In R, you can do something like that: