There's no question that the primary purpose of the morning parade is a military display. The civilian floats that follow soften things up, but are still geared to promoting Look what the Party has done for the Nation. The military focus of the parade does 3 things:

1) Internally, gives the military a formal public outlet to strut its stuff. There are a lot of generals that need validation of their worth and an outlet for their craft.
2) Internally, gives the message to the Chinese people "We the Party are in charge and the Nation is safe with us". And that is indeed the message most Chinese (well the Hans at least) seem to pick up on. To be sure, minorities in China might have a different take on this.
3) Externally, sends the message to outsiders that the Chinese are "Ready to Rumble" should the need arise. If foreigners take this to be a subtle threat, the Chinese certainly don't mind that interpretation. Though of course, they will officially disavow this purpose.

Interestingly, of the foreign diplomatic community, the only ones the Chinese invite--for protocol reasons--to the morning festivities are Ambassadors and Embassy Defense Attaches (and their wives), though they are unofficially encouraged NOT to attend. And for various logistical reasons, few do. More of the diplomatic community attend the evening ceremonies, which are the "soft fuzzy side" of the Day's Festivities and involve more popular Chinese stars.

For those of you madly interested in these sorts of spectacles, but who didn't have CCTV continuous coverage, DVD's in both Chinese- and English-language versions, including fireworks, will be forthcoming.