Well ... all three of these, really.

In essence, playing wargaming is using toy soldiers to try to re-create a little of the feel and flavour of what it was like to command a battle at some previous period in history. Sometimes these wargames are re-fights of specific historical battles, researched in depth, and carefully calculated. Sometimes they are non-specific, that is, the sort of battle that might have occurred, unrecorded in the historical sources. Often they are games that could never have occurred, because of geographical constraints, or because the armies concerned occurred in different periods of history.

This last is possible (although highly speculative) because all the troops are measured by means of certain categories, measuring how they fought, moved and reacted to enemy: and within those constraints of measurement, it is possible to measure the effect that they would have had on each other.

Because of the improvements in Weapons Technology, wargaming is divided into historical periods (with some overlapping) - as there is no joy in trying to take a Roman Legion up against WW2 stormtroopers for instance, the technological shift is too great. These periods are usually split up as follows:

Ancients - from the dawn of civilisation, until the first effective use of gunpowder on the field of battle (roughly
    3000 BC through to 1500 AD)
Renaissance - from the birth of gunpowder warfare, until the development of standardised, professional field
    armies. (1500 AD to 1700 AD)
Horse & Musket - from the emergence of professional field armies, until the development of breechloading
    weapons. (1700 AD to 1850 AD): often divided into Marlburian, Seven Years War/War of Independance, and
    Napoleonic.
Colonial - from the introduction of breechloading weapons, until the full development of automatic weapons
    and improved artillery (1850 - 1914 AD): mostly the colonial wars of imperial powers, and the American Civil War.
WW1 - the period of first full industrialised warfare (1914 - 1925).
WW2 - the period of warfare dominated by tanks and propellor plannes (1915-1950)
Modern - warfare since the development of jets, missiles, and computer assistance (1950+).

In addition, there are numerous sets of wargaming rules set in specific science fiction novels, and works of fantasy.

In essence, with any wargame, two or more players - typically two - agree on a period, and set of rules, and a day to play: each announces what army they will bring, then prior to the game calculates secretly what the composition of this army will be. On the day, they set up terrain (hills, woods, villages and so on) on a broad table - at least 6ftx4ft - and then secretly work out how to array their troops on this board.

Once that is done, they lay out their troops then (usually in alternating turns) move their troops, and calculate the effects of shooting and fighting. The rules they have agreed on will tell them how far their troops can move in a single turn, and other movement restrictions, and how to calculate what happens when their troops shoot and fight. The rules also specify what is required for one player or the other to win.

This may sound as sterile as chess can be, but in fact it is intensely absorbing: a good player needs to be able to see into his opponents mind, estimate what his plans are, then counteract them, while all the time executing his own plans to discomfort his opponents' troops.