Could someone help me understand the "Trail of Tears"?

The Trail of Tears usually refers to the Cherokee Removal in 1838-9, but it's important to remember that many nations suffered their own trail of tears during the Removal Era. This period began with the passage of the Indian Removal Act in 1830 and affected most Native people between the Appalachian Mountains and the Mississippi River.The Cherokee tend to get most attention, followed by the other four major nations of the southeast: the Creek, Seminole, Choctaw, and Chickasaw. Though often overlooked, Removal policies also affected people living north of the Ohio River, including the Shawnee and the Wyandot (the first and last, respectively, to be removed from north of the Ohio). All of those affected walked their own Trail of Tears and while they all have tales of suffering and hardship, each experience was unique.

That said, I'll be focusing on the Cherokee here because 1) their removal is probably the one you're most interested in, 2) it's the one I know the most about, and 3) information about it is more readily available.

Prior to their Removal, the Cherokee were an independent nation and in the early 1800s were moving swiftly toward the same republican-style government adopted earlier by the United States. The Choctaw, Chickasaw and Creeks were as well, by the Cherokee were a little further along on the process. As for the Seminole, they emerged as the opposition faction to the dominant Creek political elite, eventually resulting in a civil war and the separation of the two groups.

By 1830, the Cherokee had established their national capital at New Echota, drafted their constitution (it wouldn't be officially ratified until after the Removal crisis had passed), established courts, a police force, a national (and bilingual) newspaper, and so on. Much of Cherokee culture would have been quite familiar to Euro-Americans from the east. There were some Euro-Ameicans living within the Cherokee nation and a sizable portion of Cherokee with some Euro-American ancestry (about a quarter if I remember correctly), but while the US thought the Cherokee were part of their nation, the Cherokee saw themselves as an independent state.

The Removal Crisis caused considerable debate within the nation. The majority of Cherokee, Principal Chief John Ross among them, disapproved of any removal plan. A politically powerful minority, known as the Ridge Party after the Ridge family that led them, eventually came to favor Removal, taking the stance that the only way to preserve the independence of their nation was get as far from the US as they could. On December 29, 1835, the Ridge Party signed the Treaty of New Echota, which ceded the remainder of Cherokee territory east of the Mississippi and set a deadline for removal. Despite John Ross' protests and 16,000 signatures on a petition demonstrating that the treaty did not represent the position of the Cherokee majority, Congress narrowly ratified the treaty.

In spring of 1838, the deadline for removal was up and only a few Cherokee had already left. Most held out hope for an 11th hour victory (for a while, it was hoped that they could appeal to Jackson's successor, but President Van Buren upheld Jackson's position). US troops (state militia for the most part) marched across the Cherokee border to forcibly evict the more than 16,000 that remained. This was when people were forced from their homes at gunpoint as you said and sent to interment camps to await deportation. They spent most the summer in these camps, in part because John Ross continued to delay the process hoping to stop it completely. He used the presence of diseases in the camps and the necessity for medicine that would have been unavailable while traveling as the excuse to keep his nation within their own borders a little longer. The plan backfired, as the close confines of the camps caused diseases to spread and the delay eventually meant that most of the Cherokee took the journey west in late autumn and winter. Upwards of a quarter of the Cherokee population died as a result of those diseases, lack of food, and poor traveling conditions.

Since you mentioned Cherokee clothing and homes in part of your perception of the events, I thought I would also include a bit about that along with the summary of events. Conveniently the New Echota Museum has a display depicting Cherokee fashion in the 1540s, when they likely first encountered Europeans (specifically de Soto's entrada) and in the 1830s. You'll notice that cotton fabrics had replaced skins and leathers in the intervening time. As for Cherokee buildings, most lived in cabins like many of their Euro-American contemporaries. Wealthy Cherokee, including John Ross and Major Ridge, owned large Southern-style plantations, unfortunately adopting Southern slave practices to support such luxury.

Check out Theda Perdue's The Cherokee Removal and The Cherokee Nation and the Trail of Tears for more information. Alternatively, if you'd like a documentary, find PBS' We Shall Remain: Trail of Tears.

EDIT: One thing that fell out of this post was the fact that none of the Removals were absolute. A couple thousand Cherokee remained within the borders of the old Cherokee nation, either because they agreed to renounce their Cherokee citizenship in favor of US citizenship, because they were living on relatively undesirable land in the northern part of the Cherokee nation and escaped the notice of the militias that came to evict them, or because they managed to flee into the surrounding countryside until it was safe to settle down again. The descendants of those who managed to remain in their homeland despite Removal are now the Eastern Band of Cherokee.