Paraguay shares a border with both Brazil and Argentina.

Explanation:
Paraguay is the correct answer because it is the only country that shares a border with both Brazil and Argentina.

- Border with Brazil:
Paraguay shares a border with Brazil to the east. The border between the two countries stretches for approximately 1,339 kilometers (832 miles) and is marked by the Paraná River. This river serves as a natural boundary between the two nations.

- Border with Argentina:
Paraguay also shares a border with Argentina to the south. The border between the two countries extends for about 1,880 kilometers (1,168 miles) and is delineated by the Paraná River as well. This river separates the two countries and forms a natural boundary.

- Importance of Paraguay's Location:
Paraguay's geographical location is significant as it provides it with access to both the Atlantic Ocean through Brazil and the Paraguay River, as well as the Paraná River, which is a vital transportation route for trade and commerce in South America. Paraguay's strategic position as a landlocked country with access to multiple waterways has contributed to its economic development and trade relations with its neighboring countries.

- Other Options:
Colombia and Peru do not share borders with either Brazil or Argentina. Colombia is located in the northern part of South America, while Peru is situated to the west of Brazil and Argentina.

Therefore, the correct answer is option 'C' - Paraguay.