I recommend you have a look at the Collins Cobuild explanations: http://www.collinsdictionary.com/dictionary/english/especially http://www.collinsdictionary.com/dictionary/english/specially I think they are very good.

"Especially" is used to single something out, like a person or a thing. So if i meet a group of people and I like them, but i specifically like the person named Mike in that group, I might say "I liked that group, especially Mike." "Specially" means for a special purpose. If I bought a gift for you, and I normally don't by people gifts, I might say "I bought this specially for you."

Especially means "very", "extremely" The beverage wasn't especially good." Specially means "Particularly" We don't want to be treated "Specially."

Grant's answer explains the difference best :)

Special means "particular", distinguished in a distinct way. Especially means exceptional, noteworthy. PS: In the sense of "particular" or "particularly" the words mean pretty much the same thing. Often they can be used synonymously. If you need help on learning english, feel free to contact me, I'm a community tutor :) Se precisar de ajuda para aprender inglês, sinta- se à vontade para me contatar, eu sou tutora aqui no italki :)