'Specially' means that something is for a specific purpose. e.g. Tina has very small feet so she must have shoes specially made for her. 'Especially' means 'in partcular', 'even more'. e.g. I like all fruit but I especially like strawberries.

EDIT - please refer to Claire's answer below, it is the best. I am amending this answer accordingly: 'specially' is not used except in the case of how something was done (it was specially done for that particular case). whereas, especially is to describe an extent of something, or in which circumstances something even more particularly applies. ((A) I like this especially well, (B) I feel good, especially when I go home,)

In terms of usage Ian is right and 'specially' is a very rare word. Frank's defintion is fine but I guess if you had wanted that kind of answer you could have looked in a dictionary yourself. The reason that these words cause confusion, I think, is that when it is used in spoken English the 'e' sound from 'especially' is not pronounced strongly or not pronounced at all. This has meant that the words have become interchangable when speaking... When writing you should be careful though, it will normally be 'especially' you mean but Frank's first definition of 'specially' does contain some valid examples of times that you should use 'specially'.

correct spelling and incorrect`

Hailey, these two example are the best on the page. You should have posted it as an answer. Then I could have given you a thumbs up. :-)