Every now and then I'll find a word that really surprises me that it has Semitic origins. Mattress is one of them.
From the Online Etymological Dictionary:
c.1290, from O.Fr. materas, from It. materasso, from M.L. matracium, borrowed in Sicily from Ar. al-matrah "the cushion" (cf. Sp. almadraque "mattress"), lit. "the thing thrown down," from taraha "he threw (down)."
What is not surprising is that the Arabic root has Hebrew and Aramaic cognates. The parallel Hebrew root is טרח - which originally meant "to throw, put". This developed into the sense of "to take pains, to take trouble", and gives us words like tircha טרחה - "trouble, bother".
Klein connects טרח with another root - טרה. In Aramaic this root means "to take" and is the source of the phrase shakla v'tarya שקלא וטריא - the "give and take" that we find in Talmudic discussions.
Jastrow also associates טרח with another similar sounding root - טרד. This makes sense both in terms of sound, as well as meaning, for טרד, like טרח, means "to trouble". He says that all three roots are have the meaning of "to set in motion, to shake". According to him, both טרד and טרה (or טרי) have the meaning "to drip" in the Babylonian Talmud (see Niddah 49b, Bechorot 44a, Tamid 32b, Shabbat 108b.)
According to both Jastrow and Steinberg, this meaning - "to drip" - is the root of the word matar מטר - "rain". From this source, Eliezer Ben-Yehuda coined the Hebrew word for umbrella, מטריה mitriya. (Matara מטרה, however, meaning target, comes from נטר - "to guard".)
The Hebrew word טרי tari - "fresh" in Modern Hebrew - may be connected as well. Even-Shoshan in his Concordance defines tari as "wet, dripping". Klein, however, disagrees, and claims it is related to the word terem טרם - "before".
As a side note, two other uncommon words in English have their root in the Arabic taraha.
Tare means "the difference between gross and net weight". What is left is "deducted, rejected" and the word taraha can also mean "to reject".
The fortune telling cards known as Tarot are said to have the same source as well. Taraha here gives us the "discarded" pile of cards.