TL;DR
Manifest Destiny encouraged American settlers to expand the frontier, which
1. displaced Native Americans, increasing racial tensions among whites and non-whites.
2. added new states to the Union that were known as "slave states," which complicated the issue of slavery.
Explanation:
First, we should ask what exactly is "<em>Manifest Destiny</em>"?
Manifest destiny was the cultural idea that the United States should expand towards the west - they were destined for bigger things, in this case, bigger territory.
So, why would Manifest Destiny eventually lead to the <em>Civil War</em>?
To oversimplify a bit here, the Civil War was the internal U.S. conflict between the northern states (the Union) and the southern states (the Confederacy). The North wanted to preserve the Union and end slavery. The South had slaves as plantation workers, so they wanted to separate from the Union and keep slavery. So how does manifest destiny fit into this?
The idea of Manifest Destiny encouraged settlers to move west. While doing so, they encountered Native American tribes who were already present on the continent. The U.S. government and the settlers decided to relocate these Native Americans away from settler lands. American settlers had this ingrained idea of "us" vs. "them" or "whites" vs. "non-whites," which is related to the issue of slavery.
On that note, as settlers and explorers claimed new lands, they eventually formed new states that would be part of the South. When tensions on the issue of slavery began to rise, people asked, "Should slavery be permitted?" which led to another important question, "<em>Where</em> should slavery be permitted?" Should slavery be permitted everywhere in the U.S? or just the South? Slave-owners had a larger "stage" to act on- more slave states mean more territory, resources, and, most importantly, people.
Manifest Destiny enabled the U.S. to acquire more territory, and people took the idea even further: that the U.S. was <em>destined</em> to be an all white-country, no matter the place.
