-al is a common English suffix that can change nouns to adjectives and verbs to nouns.
Nouns to Adjectives:
From the Latin -alis, coming to us through Old French in the form of -el and -al, a modifier of nouns with the general meaning of 'having to do with'. 'Accident' into 'accidental'; 'nature' into 'natural', and so forth.
Some words have more twisted etymologies, having been folded, spindled, and mutilated to fit into this pattern. Aerial comes from the Latin adjective ærius (airy), and was given a redundant -al in the 1600s because it sounded better. Bridal was originally an Old English noun, brydealo, meaning a wedding feast (literally 'bride ale'); it slowly morphed into bridal, after which it started being used as an adjective referring to anything having to do with brides.
Latin had two different endings performing this modification: -alis is the default ending, but if the root word contains an 'L', the alternate ending is -aris. Thus, corporalis, but familiaris. In English this rule is sometimes bent, so while we do have familiar, we also have familial.
Well, technically, Latin had three common ways of modifying nouns to adjectives; there was also -icus, which comes to us as -ic. We have a lot of adjectives ending in -ic; metallic, poetic, archaic, public, etc. We also, as it happens, have a lot of adjectives ending in the combination -ical. So we have both historic and historical, economic and economical, diabolic and diabolical. There does not seem to be any rule to the different meanings given to the different forms of these adjectives.
Verbs to Nouns:
From the Latin -alia, the counterpart to the -alis talked about above. The suffix -alia is specifically used for the neuter plural noun counterparts of -alis adjectives. You can still see the original Latin ending in words like regalia (from regalis, meaning 'royal') and paraphernalia (from paraphernalis, meaning 'having to do with a woman's possessions, but not including her dowry'. Latin is fun!)
Once again, the French language filtered our Latin, so we use a simple -al*. Deny becomes denial; refuse becomes refusal. Many of these -al nouns didn't enter English language until a hundred years or so after the corresponding root verbs, although we seem to have stopped creating new -al nouns in recent centuries (let me know if you find any within the last 200 years. I couldn't find any).
-al is also a suffix used in chemistry indicating that a compound contains an aldehyde group. It is most likely simply a shortening of aldehyde, which is in turn a contraction of "alcohol dehydrogenatum" (dehydrogenated alcohol). 'Aldehyde' as a word did not appear until 1872 (created by German chemist Justus von Liebig), making it the newest of the -al suffixes.
My chemistry is very poor, so I will just say here that the -al suffix indicates that a molecule has a specific group attached to it, a group consisting of one carbon atom, one hydrogen, and one oxygen. The carbon is the nexus, with four connections, one to the hydrogen, two to the oxygen, and one to the rest of the molecule, whatever it be. The oxygen hogs the electrons in the group, making the group polar.
Due to the chaos of the universe, chemical nomenclature is burdened with redundancies. Butanal is also known as Butyraldehyde, methanal as formaldehyde, ethanal as acetaldehyde. (Pay attention! Methanal does not equal methanol, nor ethanal equal ethanol).
* The French also used -le, and so we also use -le in some cases, like in cattle and battle.
Webster's Third New International Dictionary, 1981
Wikipedia.org helped greatly with the chemistry.