Something that's doable can be achieved or is possible. You might be certain your plan to ride your bike across the country is doable, while your friends and family aren't so sure.
Learning to speak a new language might feel impossible at first, but you'll soon realize it's doable, especially if you find people to practice speaking with. While keeping 200 cats in your house would be utterly unworkable, keeping two cats is completely doable. Though the adjective doable has been in use since the 15th century, today it's considered to be an informal word.