In the future, teachers will certainly have to again explain the difference between impeachment and removal from office. Even now, people seem to be quite confused by the subject, despite there being a great deal written about it lately. To clarify, impeachment is a process where the Senate examines the charges brought against a President by the House. The Senate can call forth its own witnesses, examine evidence, deliberate, and then vote on the matter. Think of it like the difference between a grand jury and a criminal court. The House is like the grand jury, which examines the evidence to see if there is enough for the case to be brought to trial. The Senate then holds the actual trial.
Unlike criminal trials, the Senate acts as judge, prosecutor, defence, and jury. While jury trials usually require a unanimous decision and Supreme Court trials require a simple minority for conviction, impeachments cut the difference, requiring a supermajority (in this case 67 senators would be required) to remove the President from office. This is unlikely to happen in this case as Republicans currently hold 53 of the seats in the Senate. On an interesting side note, impeachment and removal do not, by themselves, disqualify the person removed from being voted into office again. That requires a second vote in the Senate (this time a simple majority) to bar a person from serving in office (elected or appointed) again.
It also should be noted that removing President Trump from office (let alone impeaching him) does not "undo the last election." Following the rules of succession, Vice President Pence would be elevated to the Presidency. Should that be the case (in the extremely unlikely event that the Senate votes for removal), it would be unsurprising to see Pence then pardon Trump of all charges like Ford did with Nixon (who was not impeached, but resigned before the vote for impeachment was held). Interestingly, should Trump not be removed and then a Democrat be elected President in the upcoming election (and thus, no pardon), there is a high probability that Trump could then face criminal charges for some of the actions he is being accused of doing.
As I said, this is a historic event, but it will certainly not be limited to a just day.