One are is exactly 100 square metres — a square ten metres on a side. The unit is little used today in its own right, but it is the root the hectare is built from, and knowing it makes the whole metric land system fall into place.
About the units
The are was introduced during the French metric reforms of the 1790s as the base unit of land area, from the Latin area. It never established itself at that scale, and the hectare — a hundred ares — took over instead, because a hundred square metres turned out to be too small for most land transactions. The are survives in a few national land registers, notably in parts of central Europe and in Indonesia, and in the Nordic countries it appears occasionally for garden plots. Its main modern function is etymological: hectare means a hundred ares, and the word makes no sense without it.
The exact factor
The factor is exactly 100. A square ten metres on a side has an area of 10 × 10 = 100 m². From there the family is straightforward: 100 ares to the hectare, since a hectare's side is ten times an are's; and 10,000 ares to the square kilometre. The decare, ten ares or 1,000 m², is used in Norway and in Turkey and appears in some agricultural data under the name dekar or dunam, though the dunam has several regional values.
Where you meet this conversion
Land registers in some European countries record plot sizes in ares, so a Czech or Polish property document may list an area of 8 ares where a Swedish one would say 800 m². Garden allotments and small building plots are the typical scale. Anyone reading central European property listings meets the unit regularly and needs the factor to compare against listings elsewhere. In agricultural statistics the decare appears more often than the are itself, particularly in Norwegian and Turkish data.