The Mishnah deals with the eight sheratzim - the eight crawling and creeping creatures listed in Parashas Shemini. The law regarding these eight species is that when they die they convey tumah through contact alone, and not through carrying. In this they differ from a neveilah - the carcass of a large animal - which conveys tumah not only to one who touches it, but even to one who carries it without touching it at all.
Our Mishnah goes on to discuss the laws of Shabbos as they apply to those same eight sheratzim.
"Shemonah sheratzim ha'amurim baTorah - hatzadan chayav":
One who traps one of the eight sheratzim listed in the Torah in Parashas Shemini is liable, because these species are of the kind that is normally trapped, that is, it is the way of the world to trap them. This is not the case with other species, which are not normally trapped, and trapping them is an unusual act; therefore it does not constitute the melachah of trapping.
"V'hachovel bahen chayav":
One who makes a bruise beneath the skin of one of them - the blood leaves its place and gathers there, and does not seep further, since the eight sheratzim are considered to have a hide. Two reasons are given for this liability:
Netilas neshamah (taking a life): By drawing the blood out of the system, a person takes away part of the creature's life force, and this is one of the thirty nine forbidden melachos.
Dyeing: According to several of the explanations of our Mishnah, the bruise is considered a form of dyeing - the dyeing of the hide.
Other creeping and crawling creatures:
One who wounds the other sheratzim, those outside these eight categories, is exempt, since they are not considered to have a hide under which the blood can gather. There is a dispute in a case where the blood itself actually came out and did not remain beneath the skin, whether there is liability in such a case as there is with the eight sheratzim.
And regarding the trapping of these species:
For a purpose - liable: One who traps them for a particular purpose, such as for medicinal needs and the like, is liable.
Not for a purpose - exempt: If the trapping serves no particular purpose, then since these species are not normally trapped, he is exempt.
"Chayah v'of shebirshuso":
From here the Mishnah moves on to larger animals. A non domesticated animal or a bird that is in a person's domain, that is, within his area and under his control - one who traps them is exempt, for they have already been trapped and stand in his domain, and seizing them does not constitute a new act of trapping. However, one who wounds them is liable: since they have a hide, one who makes a bruise in them is liable - either because of netilas neshamah, taking part of the life force, or because of dyeing the hide, according to the reasons mentioned above.
In summary: In this Mishnah we learned that the eight sheratzim mentioned in the Torah convey tumah through contact and not through carrying, and that one who traps them or wounds them is liable - trapping, because they are of the kind that is normally trapped, and wounding, because they have a hide, whether on account of netilas neshamah or on account of dyeing. With other creeping and crawling creatures, one who wounds them is exempt, since they have no hide, and trapping them is only a liable act when it is done for a purpose. And with an animal or bird that is in his domain - one who traps them is exempt, since they have already been trapped, and one who wounds them is liable.