Ratification is the confirmation of a treaty.
Treaties are signed by members of the government of a country. Many treaties make a country do something, or change the law of the countries which agree to it. Therefore some countries can only ratify a treaty if it is confirmed by the legislature of the country, or by a referendum (a vote of the people).
In the past treaties were signed by delegates chosen by the ruler of a country. To make sure that the treaty was acceptable to the ruler the treaty would not take effect until it was ratified by the ruler.
The United States is only bound by a treaty if the Senate agrees. So although President Woodrow Wilson signed the Treaty of Versailles which ended the First World War with Germany and set up the League of Nations the treaty never took effect for the USA because the US Senate never gave its "advice and consent" (agreed) to the treaty. This is why there was a separate peace treaty between Germany and the USA
In the United Kingdom the government ratifies treaties, it does not need the agreement of the House of Commons. However if the treaty is going to change the law then a separate act of parliament is needed. For example before Britain entered the European Union in 1973 the European Communities Act had to be passed to make the changes to the law that were needed.