**Core Concept**
Heparin is a low-molecular-weight, highly sulfated glycosaminoglycan that acts as an anticoagulant by enhancing the inhibitory effects of antithrombin III (ATIII) on coagulation factor activity. Specifically, heparin accelerates the inhibition of thrombin (factor IIa) and factor Xa by ATIII.

**Why the Correct Answer is Right**
Heparin binds to ATIII, forming a complex that accelerates the inactivation of thrombin and factor Xa. This complex is a potent inhibitor of the coagulation cascade, preventing the formation of thrombin and subsequent fibrin clot formation. The binding of heparin to ATIII is a high-affinity interaction that increases the rate of inactivation of thrombin and factor Xa, thereby exerting its anticoagulant effects.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because heparin does not directly activate the coagulation cascade; instead, it inhibits it by enhancing the activity of ATIII.

**Option B:** This option is incorrect because heparin does not directly activate platelets; its primary mechanism of action is through the enhancement of ATIII activity.

**Option C:** This option is incorrect because heparin does not directly activate the fibrinolytic system; its primary mechanism of action is through the inhibition of the coagulation cascade.

**Clinical Pearl / High-Yield Fact**
It's essential to note that heparin-induced thrombocytopenia (HIT) is a paradoxical condition where heparin administration leads to a decrease in platelet count, often resulting in thrombotic complications. This condition is a classic exam trap and requires prompt recognition and management.

**Correct Answer:** C.