When Jefferson says that the things you refer to in this question are “self-evident” he means that they are completely obvious. They do not need to be explained or proven. This is convenient, because there is no way to prove that there is such a thing as the “laws of nature” or that people have “unalienable rights.”
The idea that there are laws of nature, or natural law, came to Jefferson through thinkers of the Enlightenment. So did the idea that natural law says that human beings have certain rights by the very fact that they are human. In the thinking of men like John Locke, it was clear that the laws made by human beings (at that time, this mainly meant laws made by monarchs) were not necessarily just. Locke and others felt that there was a higher law that superseded laws made by people.
Locke then went on to set out what these natural laws said. He argued that the laws of nature said that people had certain rights that belonged to them by nature and not because government gave people those rights. He believed that the three most important rights were the rights to your life (not to be killed), to your liberty (not to be enslaved or controlled by others), and to your property (not to have your things stolen from you). Without government, the only way to protect these rights was to be strong enough to force others to respect them. Because people wanted to protect their natural rights, they created governments. This means that the government did not give them their rights and therefore had no authority to take away their rights. In other words, the rights are “unalienable,” meaning that they cannot be taken (or given) away. The “laws of nature” are laws that come from God or from our humanity (depending on your religious beliefs) and not from human beings. They are unalienable because no Earthly power has the right to take them away from us.
Jefferson had to say that these things are self-evident because there is no way to prove them. We cannot prove the existence of God (or the gods). We cannot prove that people inherently have the right to their life, liberty, and property. We can only assert that this is so. Since Jefferson could not prove that we have these rights, he had to, in essence, say that it was obvious that we have them.
It is well-known that the authors of the Declaration and the Founders in general were not always consistent about these ideals. The obvious evidence of this is the fact that they almost all supported the system of slavery, in which they systematically deprived a race of people of their liberty, property, and (at times), lives.