The impersonal pronoun il ('it') is used in French when an action has no agent, that is, when there is no person or animate being responsible for the action. The conjugated verb is always in the third person singular, no matter what tense the impersonal verb takes.
The action of the verb (pleut, 'is raining') is an impersonal, natural force. The impersonal pronoun il is often referred to as a 'dummy subject' because it fills the syntactic position of subject but doesn't have any real meaning.
Weather expressions in both French and English require impersonal subjects. The infinitive of 'weather verbs' can only be conjugated in the third person singular form (the il form).
Weather conditions are also expressed in French using the verb faire followed by an adjective or noun. Of course, when the verb faire is used impersonally in such weather expressions, it can only be conjugated in the third person singular form (il fait). See faire expressions for a more complete list of weather expressions.
Il fait chaud. It's hot.
Il fait du vent. It's windy.
Il fait beau. It's beautiful.
The verb falloir only exists in the impersonal form (il faut). It always expresses the notion of necessity or obligation which is translated into English in various ways ('must,' 'should,' 'have to'). Falloir may be followed by an infinitive as in (d), by a noun as in (c), or by a subordinate clause introduced by que as in (a); note that the verb in the subordinate clause in (a) requires the subjunctive mood. Finally, it may be preceded by a pronoun acting as an indirect object as in (b), a way to avoid the subjunctive.
The impersonal subject il may appear with the verb être followed by an adjective and an infinitive. Note that the infinitive is always introduced by the preposition de in such impersonal expressions:
Il est + [adjective] + de + [infinitive]
Other common impersonal expressions: Il y a, there is, there are
il est + clock time (Il est deux heures, It's two o'clock.)
Il s'agit de, to be about, to be a matter of, to be a question of
Il vaut mieux, to be better, to be advisable