From Chabad.org: The first Aliya discusses the Kohen‘s obligation to maintain a high level of ritual purity, and the women he may marry. An ordinary Kohen is prohibited to come in contact with a human corpse — except to attend the funerals of his next of kin — and may not marry a divorcee as well as some other women. The High Priest is not permitted to attend even family funerals, and is required to marry a virgin.
Although less relevant to us because it discusses rules for Kohanim when they served in the Mishkan, there are some interesting tidbits hidden in this Aliya. For example, the Kohen Gadol (high priest) was forbidden from leaving his hair uncut for longer than 30 days (according to a Gemara in Sanhedrin) because it was a gesture of mourning. The rule is interesting, but it’s interesting that this rule is given only to the Kohel Gadol. A lot was conveyed by the priests through appearance through the special garments he wore, but this is the first time his physical appearance was deemed significant enough to monitor. Is it superficial to worry about looks, or can we really convey an attitude with the way we look, and thus have a responsibility to maintain appropriate appearance? Apparently the latter, which I wouldn’t have thought the Torah cared about until this Aliya.