This is, of course, a matter of how you personally interpret what's going on in this speech.
In my opinion, the way Lord Capulet speaks of storms is meant as a commentary on Juliet's emotions and on the emotions of women in general. There is a stereotype of women that says they are emotional and not really in control of those emotions. I think that Lord Capulet is using that stereotype here.
He tells Juliet that she is like a storm. By saying that, he is saying that she is uncontrollable. He cannot control her and, it appears, neither can she control herself.
So, I'd say the significance is that it shows Lord Capulet's view of how men are better and more in control than women.
Traditionally in literature, and specifically in Shakespeare, the use of storms is a form of foreshadowing. Because staging a storm is challenging, especially in the 1500's writers, like Shakespeare use dialogue to show and explain what is happening.
Although in this specific scene the reference to the storms refer to Juliet's crying which Lord Capulet compares to storm which comes because Juliet does not like the news that she is to wed to Paris.
Capulet compares Juliet's tears to the storm and her body as a bark floating and being beaten by the water. He ends his discussion of the storm saying, "Who,--raging with thy tears, and they with/ them,--/Without a sudden calm, will overset/Thy tempest-tossed body."
This image of a tossed body can be interpreted as a dead body, which will eventually be Juliet's. Also, it is Capulet's way of saying Juliet is overreacting the news that she will be married to a nobleman; news she should consider as making herself lucky.
Finally to emphasize that this discussion of a storm is foreshadowing, Capulet exits the scene after telling Juliet and Lady Capulet that Juliet is "For by soul, I'll ne'er acknowelge thee," a statement implying that Juliet will be dead to him if she doesn't marry Paris. This, of course, happens when Juliet choses to marry Romeo instead.