Iphone will not accept my gmail password

My phone and my mail was working fine until about 3am yesterday. Now it suddenly says my name and password are wrong. imap.gmail.com- says it is incorrect.

1) I try to enter the password again, it still says it is wrong.

2) I went on my computer to use gmail- it lets me in using my password.

3) I updated the software to 5IOS, thinking there was a glitch-the phone was restored in the proceess. After the update, it still does not accept my password.

4) I changed my password on my computer. Iphone still does not accept the new password.

5) I deleted the account, then put it back in with the password, says it will not accept it- so now I have no email account on my phone.

6) I turned off the phone and turned it on again.

None of these things worked, clearly. What am I doing wrong and why did my iphone suddenly decide it did not like my password?