The first paragraph of the Declaration is its Preamble, that is its introduction and statement of purpose. Preambles are quite common in many legal documents, they typically (but not always) begin with "whereas...." Jefferson wished to properly introduce the topic, and inform those reading the document that it was necessary for those declaring their independence to state their reasons why. Its language has no particular legal significance; it is merely informative. The rest of the document, of course, is based on Locke's Second Treatise on Civil Government in which Jefferson explains the right of the colonies to declare their independence, and their reasons therefor.
The first paragraph of the Declaration of Independence does not have a major significance. It is simply an introductory paragraph telling what the purpose of the document is.
The first paragraph first states that the colonies are going to become independent -- they are going to
dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them...
By saying this, the authors of the Declaration state what they are going to do -- they are going to break away from England. This is the most important purpose of the first paragraph.
The rest of the paragraph simply says that the authors feel that they need to tell why they are breaking away from England. By saying this, they are introducing the next part of the Declaration, which is much more important because it states the political philosophy that underlies their rebellion.
So, the purpose of the first paragraph is to state what they are going to do (declare independence) and state that they are now going to say why they are doing it.