Well, for one of several reasons. It might be because it means NOT-something-beginning-with-an-L. An example is the word aliterate (which describes someone who can read but is disinclined to do so). The a- bit means not in Greek. (Though of course the AL in the word almighty means, well, more or less the opposite: it's short for all. Always and alone are to do with ALL, too.)
A word might begin with AL because it means IN THE STATE OF something beginning with L, such as alive.
Alack is quite similar, though it's short for Ah! Lack!
A word might begin with AL because the word's borrowed from a foreign language. Aliyah, which means immigration to the Holy Land, is the Hebrew word for the act of ascending (for those who like such things, it has a cool plural: aliyoth). Albino comes from the Latin albus, which means white.
Quite a lot of these foreign words begin with with AL because they come from Arabic, and al is the Arabic for the. Some of these words are outstandingly cool, such as the sea fish the albacore, which comes from al+bakr, which means the young camel; albatross, from al+ghattās, means the white-tailed sea-eagle; alcohol, which comes from al+kuhl, the powdered antimony; alcove from al+qubbah, the vault or arch; and Almagest (a mediaeval book on astronomy or astrology) comes from al+majisti, which simply means the greatest.
Sadly, the word alkahest is the invention of our old enemy Paracelsus the bighead, who made up the word to describe the universal solvent sought by alchemists (there's another one! It comes from al+kīmiyā, the transmutation). It seems that he did this just because it looked really quite cool.
Word To Use Today: one beginning with AL.