Chewables are generally flavored, to entice the patient to be compliant with their medication regimen, which are usually children. Many children do not like taking meds, and if the meds look and taste more like candy than meds, then logic predicts the child will take their meds without too much fuss. There are some antacids that are chewable. Chewing helps dissolve these meds.
As for those meds that should be swallowed, chewing these will usually result in a bitter-tasting, non-pleasant experience that may cause you to vomit, if not gag. Chewing prior to swallowing may make the drug less effective due to enzymes found in saliva. Yet, it is believed that this action produces negligible change of the medication, and it is still fairly effective. Take caution, however, some drugs may stain teeth or weaken the enamel. As a rule of thumb, read the instructions before taking any meds, and FOLLOW exactly.
mlmar makes a good point. Extended release, or delayed action pills need to be swallowed because they are specially manufactured to slowly dissolve in the stomach or intestines, and chewing it will degrade the medication quicker as it destroys the coating and/or "special" mini-compartments designed to withhold from releasing the full dose of the pill all-at-once.