Slovakia's flag is a white, blue, and red tricolor with the national coat of arms set into the hoist side. Without the arms it would be almost indistinguishable from several other Slavic flags, which is precisely why they are there.
A flag for a country that did not exist yet
The flag was adopted on September 3, 1992, ahead of the dissolution of Czechoslovakia at the end of that year. The lineage goes back further. Slovak nationalists began using a white-blue-red tricolor in the late 19th and early 20th centuries, following the pan-Slavic colors agreed at the Prague Pan-Slavic Congress of 1848, which had themselves been drawn from the Russian flag.
Slovakia had spent most of the 20th century inside Czechoslovakia. The split at the end of 1992 made a distinct national flag necessary in a hurry, and the design that emerged leaned on historical and cultural symbols already familiar to Slovaks.
The double cross and the three peaks
Three horizontal stripes of white, blue, and red, with the coat of arms placed to the left, centered vertically and reaching slightly into the blue stripe.
The arms show a silver double cross on a red background, mounted on a blue mountain of three peaks. The peaks are the Tatra, Fatra, and Matra ranges, which puts the country's geography on the flag.
The double cross comes out of Slovakia's Christian history, and specifically from the mission of Saints Cyril and Methodius in the 9th century. It is a heraldic device carrying both religious and territorial meaning, which is unusual on a modern national flag.
Usage
The flag is displayed at government events and ceremonies and on public buildings including the Presidential Palace. It is prominent on national holidays and commemorative days.
Protocol gives it the place of honor when raised alongside other flags: it goes up first and comes down last. Government bodies use slight variants to distinguish their functions, but each keeps the core design.
Similar flags and influences
Slovakia's flag resembles those of Russia and Serbia, which use the same white-blue-red tricolor from the shared pan-Slavic tradition. The Czechoslovak flag is the other obvious ancestor, since it combined elements from both Czech and Slovak territories and the colors were common to both.
References
[1] Slovakia's Ministry of Foreign Affairs: Official Government Site