A conventional loan is not insured by the government (meaning that the government does not make any guarantee that you will pay the mortgage). Therefore, carries PMI (private mortgage insurance) if you put less than 20% down. Conventional loans stick to guidelines set by Fannie Mae and Freddie Mac and are available to everyone. However, they are more difficult to qualify for than VA or FHA loans. Typically, you need a steady income and decent credit.
An FHA loan is a loan insured or protected by the Federal Housing Administration (this means that if you default, the FHA will repay the note to the bank). Due to the loan being insured, the lender usually offers a lower down payment and closing costs. Anyone can apply for an FHA loan and it is easier to qualify for than a conventional loan. Instead of PMI on your FHA loan, you will have a mortgage insurance premium which stays with the life of the loan. That means you cannot remove the insurance without refinancing the entire loan.
A VA loan is guaranteed by the Veterans Administration and is available only to certain borrowers through VA-approved lenders. Usually, you need to be in the military, have served a length of time as active duty, or are the spouse of a service member who has died in the line of duty. VA loans do not carry private mortgage insurance and there is no money down required.