This is the most likely factor of what will impact the interest you earn on a CD. When you open a CD, you need to select a length of time, usually anywhere from 6 months to 5 years, in which this money will be invested. During this time, this money will not be available to withdraw without a penalty. The longer of term you select, the higher your interest rate will be.
As with any savings, the more money you are able to invest, the more you will earn on the other end in interest. For some accounts, they have a minimum deposit amount on higher interest rate accounts in order to incentivize those who have the funds to pick their account.
The institution that you select may impact what rate of interest you receive. For example, the rates between a local credit union and national bank could differ simply based on their personal resources and goals as a company.
The interest rate of similar accounts or other benchmark rates may impact what interest rate your financial institution is offering. When federal rates rise or fall, this may also impact what happens on a local level.