|א וַיְהִי, מִקֵּץ שְׁנָתַיִם יָמִים; וּפַרְעֹה חֹלֵם, וְהִנֵּה עֹמֵד עַל-הַיְאֹר.||1 And it came to pass at the end of two full years, that Pharaoh dreamed: and, behold, he stood by the river.|
What is the implication of two full years? Well, this might in part depend on how we understand מִקֵּץ. The word מִקֵּץ means "at the end of," but does not specify the beginning of the period. This could have been from the time he was initially placed in prison, or from the time that the butler promised to bring up Yosef's case with Pharaoh, and promptly forgot (see previous verse).
If we assume the latter, there have a great reason why the specification of two full years. In the previous parsha, Vayeishev, in Bereishit 40:20:
If so, two full years later would once again be Pharaoh's birthday, and a most opportune day for Yosef to be mentioned by the butler.