We already discussed a bit on this via PM with Lannes, so here's the general outline:
"Skirites" were one of those people that were named "Perioikoi". Skiritis was a region at the North of Sparta.
My understanding is that they were farmers, living close to the border with Tegea, they contributed some 600 men to the Lacedemonian army, they fought (usually) at the extreme right of the army (it makes sense since that was the weak spot), usually moving forward to clear the way of the phalanx of enemy light troops that were hurling javelins and stones at them. So they acted same as the "ekdromoi" in other greek armies. Lightly armed troops armed only with shield (hoplon) and spear. They were able to run fast and intercept peltasts but the Hoplon allowed them to fight in phalanx formation if the need would arrise.
They were also used in a reconnaissance role and were assigned the watch task at the camp. http://www.press.umich.edu/pdf/0472110640-01.pdf
Read here Xenophon's account: http://www.globusz.com/ebooks/Cyropaedia/00000015.htm (search for Skirites)
Others indidate that they were used as "Hamippoi" light troops that supported cavalry.
My belief is that they were employed in all tasks of lightly armed troops. Sometimes as "Ekdromoi" sometimes as "Hamippoi" one time covering the left side of the phalanx another the right and on occasion doing reconnaissance...
Your views?