By using a divine focus as part of casting, you can cast any spell with a material component costing the value of that divine focus (maximum 100 gp) or less without needing that component. For example, if you use a silver holy symbol worth 25 gp, you do not have to provide material components for an arcane spell if its components are worth 25 gp or less. The casting of the spell still provokes attacks of opportunity as normal. If the spell requires a material component that costs more than the value of the divine focus, you must have the material component on hand to cast the spell, as normal.
In response to questions about the use of 'Alchemical Power Components' and whether False Focus can be used to 'supply' them:
An alchemical power component is an alchemical item used as a material component or focus for a spell in order to alter or augment the spell's normal effects. What follows is a sample of these effects using this item as a component; your GM may allow other combinations.
Spells followed by an (M) expend the alchemical item as a material component
Spells followed by an (F) use the item as a focus and do not expend it
In both cases, the alchemical item does not have its normal effect and does not affect any other parameters of the spell. You cannot use the same item as both a focus and a material component at the same time.
In response to further discussion about using multiple alchemical power components on the same spell: it is correct that multiple alchemical reagents do not stack, and multiples cannot be used on the same spell. What is incorrect, however, is the assertion that all alchemical power components are alchemical reagents. Not only is that connection never stated in the official rules sources, but also the official rules source does provide an explicit list of what the alchemical reagents are (the same rules source that says reagents don't stack, Alchemy Manual, which first introduced the term). This is a sub list of all alchemical power components, and is as shown here: