If you have two Gmail addresses, you can only be signed into one at a time from the same computer, unless you configure your account to let you do so. So if you are signed in to your main one, you have to sign out before you can sign into your other one.
I believe Yahoo is the same -- I have two Gmails and two Yahoos, and I can't quickly switch between them; I have to sign out and sign back in. Same would apply if someone else in your household uses your computer to check their email. (For example, if I want to check my Yahoo mail on my daughter's computer, I need to log her out and log myself in.)
Now, in poking around Gmail, I see that you can set it up to switch between multiple accounts -- go to "Settings" in the upper right corner, "Accounts and Import", then "Google Account Settings" at the bottom of that page. From there, you can click to edit "Multiple sign-in" and follow the instructions there.
Does that help?
Kathy
