If you want other people to access your Gmail account, you can grant the person. This is to allow others to read and send mail on your behalf. Please see below for details:
Step 1: Login your Gmail account (please refer here to open one if you do not have an account yet);
Step 2: In the Gmail account, click the "Setting" button from the right-top corner;
Step 3: Click the "Settings" command from the drop-down list;
Step 4: Click the "Accounts and Import" tab in the settings menu;
Step 5: In the "Grant access to your account" section, click "Add another account";
Step 6: Type the email address that you want to check, and click "Next Step";
Step 7: Click "Send email to grant access" in the next window to continue;