Caffeine increases the level of circulating fatty acids. This has been shown to increase the oxidation of these fuels, hence enhancing fat oxidation. Caffeine has been used for years by runners and endurance people to enhance fatty acid metabolism. It's particularly effective in those who are not habitual users.
Caffeine is not an appetite suppressant. It does affect metabolism, though it is a good question whether its use truly makes any difference during a diet. The questionable rationale for its original inclusion in diet pills was to make a poor man's amphetamine-like preparation from the non-stimulant sympathomimetic phenylpropanolamine and the stimulant caffeine. (That you end up with something very non-amphetamine like is neither here nor there.) The combination drugs were called "Dexatrim" or Dexa-whosis (as in Dexedrine) for a reason, namely, to assert its similarity in the minds of prospective buyers. However, caffeine has not been in OTC diet pills for many years per order of the FDA, which stated that there was no evidence of efficacy for such a combination.
From Goodman and Gilman's The Pharmacological Basis of Therapeutics:
Caffeine in combination with an analgesic, such as aspirin, is widely used in the treatment of ordinary types of headache. There are few data to substantiate its efficacy for this purpose. Caffeine is also used in combination with an ergot alkaloid in the treatment of migrane (Chapter 39).
Ergotamine is usually administered orally (in combination with caffeine) or sublingually [...] If a patient cannot tolerate ergotamine orally, rectal administration of a mixture of caffeine and ergotamine tartarate may be attempted.
The bioavailability [of ergotamine] after sublingual administration is also poor and is often inadequate for therapeutic purposes [...] the concurrent administration of caffeine (50-100 mg per mg of ergotamine) improves both the rate and extent of absorption [...] However, there is little correspondence between the concentration of ergotamine in plasma and the intensity or duration of therapeutic or toxic effects.
Caffeine enhances the action of the ergot alkaloids in the treatment of migrane, a discovery that must be credited to the sufferers from the disease who observed that strong coffee gave symptomatic relief, especially when combined with the ergot alkaloids. As mentioned, caffeine increases the oral and rectal absorption of ergotamine, and it is widely believed that this accounts for its enhancement of therapeutic effects.
Nowadays most of researchers believe that the stimulatory actions are attributable to the antagonism of the adenosine. Agonists at the adenosine receptors produce sedation while antagonists at these sites, like caffeine and theophylline induce stimulation, and what is even more important, the latter substance also reverse agonists-induced symptoms of sedation, thus indicating that this effects go through these receptors.
Another possibility, however, is that methylxanthines enhance release of excitatory aminoacids, like glutamate and aspartate, which are the main stimulatory neurotransmitters in the brain.
As to the side effects: methylxanthines inhibit protective activity of common antiepileptic drugs in exptl. animals in doses comparable to those used in humans when correction to the surface area is made. It should be underlined, that although tolerance develop to the stimulatory effects of theo or caffeine when administered on a chronic base, we found no tolerance to the above effects . This hazardous influence was even enhanced over time. Therefore, it should be emphasized that individuals suffering from epilepsy should avoid, or at least reduce consumption of coffee and other caffeine-containing beverages.