In order to qualify for Medicaid, a single individual cannot have more than $2,000 in countable assets, and a couple cannot have more than $101,540. Any excess must be either spent down until it's gone (not generally the best alternative), gifted (which causes a costly period of Medicaid ineligibility), or converted to a non-countable asset. Such a non-countable asset is a "Medicaid annuity." Here's how it works.
An annuity is a regular stream of payments back to you, in exchange for a lump sum of money. They can be either private (made between you and a family member) or commercial (made with an insurance company). Medicaid only allows commercial annuities.
For example, if you are a male, age 70, you could transfer $50,000 to an insurance company in exchange for a monthly annuity payment of $400, guaranteed for your life, no matter how long you lived. But what if you died unexpectedly after two years? The annuity payments would stop. Most people do not like that, and therefore will typically purchase the annuity with a "guarantee period" of at least a certain number of years.
According to the Medicaid rules, a male age 70 has a life expectancy of 12.8 years. So you cannot purchase an annuity with a guarantee period that exceeds 12.8 years without causing a period of disqualification from Medicaid. So let's stick with 12.8 years to be safe. Because you are guaranteed payments for the longer of your life expectancy or 12.8 years, the monthly payments will be lower. In this example, they drop from $400 to $354 per month.