The word were replaces was in sentences that express a wish or are contrary to fact:

Example: If Joe were here, you'd be sorry.

Shouldn't Joe be followed by was, not were, given that Joe is singular? But Joe isn't actually here, so we say were, not was. The sentence demonstrates the subjunctive mood, which is used to express things that are hypothetical, wishful, imaginary, or factually contradictory. The subjunctive mood pairs singular subjects with what we usually think of as plural verbs.

Examples:
I wish it were Friday.
She requested that he raise his hand.

In the first example, a wishful statement, not a fact, is being expressed; therefore, were, which we usually think of as a plural verb, is used with the singular it. (Technically, it is the singular subject of the object clause in the subjunctive mood: it were Friday.)
Normally, he raise would sound terrible to us. However, in the second example, where a request is being expressed, the subjunctive mood is correct.
Note: The subjunctive mood is losing ground in spoken English but should still be used in formal speech and writing.

Day 2: Verb agreement rules (slides)