When talking about "mAh (milliampere-hour)" we are speaking in regards to a rating which describes both the charge capacity and how much power a battery can output over time. A higher mAh rating would allow for longer battery life before that needs to be taken out and charged again (or in the case of a lipo-battery, before that needs to be plugged in again to charge). So, if you want to be able to use your battery for a longer amount of time before having to recharge, a higher mAh just might be what you are looking for.
*The mAh of a battery does not necessarily mean that the battery will be safer to use however, and more research on a batteries amp limits should always be done before committing to any single cell for use in your device.
For more specific battery information (depending on the type you are using) and to see good examples of baseline tests being done, Mooch's battery guides on reddit will be a very useful resource for any budding vaper looking to know more about battery safety or any day to day vaper wanting to make sure they are in the clear with the battery they are choosing.
Follow this link to find Mooch's ecf forum which is chock-full of the mentioned information: https://www.e-cigarette-forum.com/forum/blogs/mooch.256958/