In addition to the excellent summary given by the previous answer, it is important to note that witches were traditionally associated with bad weather. Specifically, many witches were accused of ruining harvests, either through flooding or drought or through their power over the weather. As a result, when Shakespeare's audience saw witches and immediately heard from them about the weather, they would understand that the witches are in charge in this environment. The witches' power over the weather is supported by what the First Witch says about the sailor, namely, that "though his bark cannot be lost / Yet it shall be tempest-tossed." She is very specific about what she has the power to do: she cannot kill the sailor herself, but she can exercise control over the weather in order to make him sleepless and miserable, just like Macbeth after he becomes king. Similarly, the witches do not actually kill anyone in Macbeth, but they manipulate Macbeth to make him murder people. Their control of the weather symbolizes their indirect control over the events of the play.

Macbeth opens with "Thunder and lightning," portents of the evil to come.  The witches enter with thunder in Act I, scenes i and iii, and again in Act IV.i.  Off stage, the thunder would have been easily created by shaking sheet metal.

The foul weather of "thunder, lightning, and rain" serves as a pathetic fallacy (attributing human feelings to inanimate objects, like weather), foreshadowing the inner storm brewing in Lady Macbeth and Macbeth.  In short, the witches are like meteorologists: they forecast the outside weather (thunder) and the internal weather (murderous thoughts of the Macbeths).

Also in Act I is the Bleeding Captain's battle recap for Duncan, which features weather imagery:

As whence the sun 'gins his reflection
Shipwrecking storms and direful thunders break,
So from that spring whence comfort seem'd to come
Discomfort swells.

The foul weather is again echoed in the murder scene of Banquo.  Just before he is besieged by the three murderers, he says to his son Fleance:

It will be rain to-night.

Thunder is sounded when the witches show Macbeth the future:

Thunder. First Apparition: an armed Head.

Thunder. Second Apparition: A bloody Child

Thunder. Third Apparition: a Child crowned, with a tree in his hand

All told, the weather imagery and stage sound effects couple to create an internal and external sense of awe, mystery, and foreboding in the minds and ears of the reader and audience.  Just ask Duncan and Banquo: when it rains, it pours blood in Macbeth.