Great question - I bet you have been reading product labels and maybe seeing some info-mercials about facial cleansers/acne treatments.
To answer your question, we have to first take a look at what "acne" is. Then we can investigate what affect sulfur might have on acne.
Acne is a pretty common skin disease that has a number of "causes" associated with it, including a hereditary component, diet, hormone levels, inflammation, and, it is often associated with bacteria in the pores (the bacteria is called Propionobacterium acnes). To find out more about acne, the Wikipedia site is a good place to start (in my opinion, Wikipedia can be an excellent starting point for answering many questions of a scientific nature, but you should never stop there). I think the acne site is pretty good because it is thorough and links to primary sources for its information: acne
Regardless of the actual cause, acne is the result of blockages in follicles by a "plug" of keratin (a skin protein) and sebum (an oil). "Whiteheads" are the result of sebaceous glands (the cells that make the oil) becoming clogged with sebum and dead skin cells. The P. acnes bacterium can then cause inflammation and small lesions in the skin, which results in redness. A "blackhead" is similar to a whitehead, except that the keratin protein in the plug is oxidized, giving it a black color.
So, why sulfur in these acne products, and what does it do?
It turns out that the sulfur is an inhibitor of growth of the P. acnes bacterium - it is a mild "antimicrobial." However, its precise mechanism of action is unknown. It is thought that the sulfur may interfere with and cause inactivation of sulfhydryl groups on the proteins involved in specific enzymatic pathways in the bacteria. For acne treatment, the sulfur is almost always combined with another antimicrobial called sodium sulfacetamide. This compound acts as a competitive antagonist to paraaminobenzoic acid (PABA), an essential component for bacterial growth.
Since most people who have acne do have some degree of inflammation due to the P. acnes bacterium, sulfur and sodium sulfacetamide are almost always included in the products to treat acne. One advantage of the topical application of antimicrobials such as sulfur is that they have very few side effects and do not lead to microbial resistance.
Sulfur will not have an effect on a person's underlying cause of acne if it involves hormonal levels or diet, (for example), but it certainly can help with the inflammation caused by the bacterium.
It would be interesting to figure out exactly how sulfur acts as a mild antimicrobial - sulfur is cheap and easily applied. This yellow, non-metallic element has been used throughout human history as a medicinal, but we don't really understand (at least to my knowledge) exactly how it exerts its antimicrobial effects.