one way they can gain access to your email accounts is by your security questions you enter if you forgot your password.
another way is by the other email account linked to your account used to also verify if you are the owner, and sometimes that secondary account is easier to hack (like a hotmail account). so they get into the easy account, then use that account to get into your more secure account.
or they can guess your password (easier if they know u)
or they can get your password used on other sites and see if it works for your email (and bank) too.
MANY ways to do it. any time you have ANY breach of security, you have to change ALL passwords and your security questions.
once they are into your email account, they can use that to reset the passwords on any other site you use. and they can find out what bank and services you use by looking at your old emails.
i had my gmail account hacked into through a less secure hotmail account. they somehow got into my hotmail account then used that to change my password for the gmail account.
i always have one password JUST for my bank and one password JUST for my email and the other sites share passwords....i have a shared higher level password, a shared medium level password, and a shared crap password for sites that dont matter and dont have any sensitive info.
my friend just had her purse stolen, and the thieves called the bank and had them change the pin over the phone and they didnt even require they use the account phone code. they just changed it for them using the info they found in her purse. and then they went on a giant spending spree and the bank refuses to cover the losses because they had a pin. but they only had a pin because the bank let them change the pin!!
and so she has to get her car rekeyed (hundreds of dollars), her house rekeyed, a new passport, id, cards and everything. and the cops wont even look into it and get the video footage from the stores they used the card at. so shes out thousands of dollars.