We're all familiar with the seder סדר on Pesach, but the word seder in regards to the Pesach meal only appears first in Rashi's Sefer HaOrah. We find seder - meaning "arrangement" - in the Mishna in a context that is not exactly kosher for Passover - in the description of the lechem hapanim (showbread) in Masechet Menachot, chapter 2.
In the Torah (Vayikra 24:6) where it discusses the lechem hapanim it uses the synonym maarechet מערכת - meaning "set, row". Onkelos translates maarechet into Aramaic as seder, and both verbs - ערך and סדר - have the same meaning - "to order, arrange".
Other meanings of seder and sidra סדרה in Rabbinic Hebrew relate to an order or set of items - the sidrot - weekly Torah portions, the six sedarim of the Mishna, and the seder hamazalot סדר המזלות - the constellations. We also find in Rabbinic Hebrew reference to seder hatefila סדר התפילה - the order of the prayers (Rosh Hashana 17b), but the more common word for the prayerbook, siddur סידור, does not appear until Medieval times.
The word seder only appears once in the Tanach - in Iyov 10:22 as סדרים sedarim. There are those that feel that the word seder entered Hebrew from Aramaic, and is also related to the Akkadian sadaru.
Another theory is that seder is related to the Hebrew word שדרה - sdera - also meaning "row" and in Melachim II 11:8 means "a row of soldiers". In modern Hebrew it also means "boulevard, avenue" and Sderot שדרות is a town in Southern Israel famous for being attacked by Kassam rockets. It got its name from the rows of trees planted there at the founding of the State.
A common mistake in Hebrew is to pronounce שדרה as shdera and שדרות as Shderot (the latter has 12,000 hits on Google, with 300 on official government sites!) This is probably due to a confusion with the word שידרה shidra - "spinal column, backbone" - which also has a sense of something straight. However, according to Klein, shidra has a very different etymology: it is related to the word שזרה shizra (dalet and zayin can interchange), also meaning "backbone", which comes from the root שזר - "to interweave, intertwine, twist".