Hey Mudcake,
A "reading" refers to applying some literary theories (though they do not have to be strictly applied in a literal sense; for example, Marxism can be both used to describe the ideas of Karl Marx, but can also be a "reading" also) that can be seen through texts.
For example...
Like Claire said, there you can read texts through a Feminist's perspective, where you examine the social roles of women, their conditions of marriage, their economic situation etc. When you read classics, like Jane Austen and Shakespeare you'll find that women live in patriarchal societies - marriage is reduced down to business transactions, they clearly play a subordinate role to men, only males are allowed to have formal educations etc etc.
But you can also look at texts and how they reflect other theories. A Marxist critic looks at the distribution of power within society and the social classes formed by economic bands. A psychoanalyst applies Freudian theories to texts; a queer theorists looks at the oppression of homosexuality through the Canon and other literary works; Post-Colonialism attempts to comprehend the problems of European colonialism on literary production, and consists of writings from countries whose experience of colonialism has shaped their political existence, under the control of a European power; Modernists look at the grand scale of change in the early 20th century and the list goes on, and on, and on! lol
Anyway, hope that helps you. It's really late.
And don't forget to add capitals, e.g. Feminism, Marxism to your reading! My teacher doesn't like it when we don't because yeah... they're movements or something, the name to certain eras...
Toodles!