An ode is generally a lyrical verse written in praise of someone. The earliest version, the Grecian ode, had three structural parts: the strophe, antistrope and epode. Other variations also existed. The Grecian ode was originally accompanied by an aulos, a double reed woodwind instrument. However, the later English odes did not specifically include the three-part structure, and tended to be a dedication to a person (or even an object, such as "Ode on a Grecian Urn") that inspired an interest in the poet. In later years, odes have often been written to honor famous people or to commemorate a special event, such as a retirement.
Like so many things, the formal definition of an ode has changed over the years. One thing that is still the same is the tone and style of this kind of poem; it is meant to be formal and dignified and is often written for a specific person or occasion. A funereal event would often be an occasion for an ode. In today's less formal world, this form is often used in parody--using that formal, dignified tone to honor something more ridiculous or inane. "Ode to a Broken Fingernail" or "An Ode to My Rusted-out Chevy" would be examples of this kind of parody. It is the contrast between a formal tone and style for something which is anything but formal which creates the irony of parody.
Another element of an ode, in addition to the formal tone, is a formal structure. As mentioned above, the form was quite precise and uniform. Today, what usually matters is that there is some structure and some rhyme scheme. An ode must have a metrical and rhyming pattern.
Aside from these two criterion, an ode is generally what you choose to make it.