This fourth aliyah contains three concepts: the Sotah ceremony in the case of the suspected adulteress, the nazir who dedicates him or herself to G-d, and the priestly blessing. The Midrash Rabba, a book of commentary, dedicates two whole volumes to just this parsha Nasso.
The Sotah ceremony concerns a woman who is suspected of adultery. The woman is brought to the priest with a certain sacrifice. The priest then uncovers the woman's hair and says a prescribed warning, in the form of a curse, to her. The warning/curse says that harm will come to her if she committed adultery, and won't come to her if she didn't. The priest then writes the curse on parchment and dissolves the ink in water, and then the woman drinks the water. If she committed adultery her belly explodes, if not, she is cleared of any suspicion. Not only is she cleared of any suspicion, but blessing comes to her: if she previously didn't have children now she will have children, if she previously had only daughters, now she will have also sons, in all cases improving her offspring.
We can learn many things from the Sotah ceremony, but one is that the ceremony includes the dissolving of G-d's Name (contained in the curse) in the water that the suspected adulteress drinks. Normally, it is forbidden to erase G-d's Name, but in this case we see that G-d is willing to have His Name dissolved in order to clear up any suspicions that a husband may have for his wife. We therefore learn how we should bend over backwards for the sake of peace between a husband and wife.
Next, in this aliyah, we have the law of the Nazarene who vows to abstain from wine and other grape products for a certain period of time, and at the end he/she brings offerings including a sin offering. This shows that although it's a holy thing to become a Nazir, to abstain from the kosher physical pleasures that G-d gives us (like wine) is somewhat of a sin.
Finally this aliyah contains the priestly blessing, which are recited by Kohanim in the synagogue on Yom Tovim. (The holiday instructions for the priestly blessing service are given on page 268 of the siddur "Tehillat Hashem".)