Proportional representation is a system under which seats in a legislative body are allocated to political parties based on their respective percentages of the vote in a country (or a political subdivision of a country). It is an alternative to the system under which a country is divided into individual districts, each of which elects one member to the legislative body.
The most pure form of proportional representation that I know of, is used in elections for Israel's parliament, which is called the Knesset. The Knesset has 120 members, none of whom represent individual districts. The voters do not vote for any individual(s); they vote for a party. A party that gets 25% of the votes gets 30 seats (25% of 120 = 30, for the math-challenged). However, a party must get at least 2% in order to be represented in the Knesset.
This is also called a "party list" system, because each party compiles a list of its candidates, with the order of the names on the list determining which individual candidates are elected. For example, in the scenario mentioned above, the top 30 names on that party's list would become Members of the Knesset (MKs).
The Knesset is a "unicameral" legislative body. In other words, there is only one house. In that sense, it is unlike the U.S. Congress and the U.K. Parliament, which are "bicameral" legislatures, in that they have two houses (in the case of the U.S. Congress, the two houses are the Senate and the House of Representatives).
Here is a link to the Knesset's own explanation of its electoral system.
An example of an electoral system diametrically opposed to that one is the method of electing representatives to the U.S. House of Representatives. The Constitution provided for direct election of representatives in the individual states in Article I, Section 2.
However, the Constitution said nothing about dividing the states into districts. A state that is so small that it is apportioned a single representative of course elects that representative on an at-large basis. But some states at some times in the past held at-large elections for multiple House seats. According to this website, federal law has gone back and forth on that subject.
The U.S. Supreme Court, in cases such as Wesberry v. Sanders, set standards for establishing the boundaries of congressional districts. One effect of these decisions has been to enshrine the concept of single-member congressional districts in constitutional law.
At-large elections tend to work to the disadvantage of minority groups. Under the federal Voting Rights Act, the so-called "majority-minority" congressional districts have been created. In other words, in the redistricting process, the states are to create as many districts as possible in which ethnic minorities comprise a majority of the voters in the district. This has increased minority representation in the House of Representatives, but it is not without controversy.