In days past, many Scottish burghs had a mercat cross (in English, a market cross) as one of their landmarks. It was a formal symbol of a town's government and its right to maintain an official marketplace, and might take the form of a wooden or stone post, although throughout the centuries they have become increasingly ornate.
The mercat cross was one of the essential features of a well-established Scottish burgh, the others being the tolbooth (or later, the town house) and the kirk (church). 'Mercat' is Scots for 'market'. The etymology of 'cross' in this case is a bit complicated; it originally meant cross, in the same sense we use it in today, but it later came to mean an official marker post, or monument used as a legal marker. The continued use of 'cross' in this context was probably reinforced by the use of the mercat cross as a trone, a large four-armed scale or balance, which was indeed cross-shaped.
Since the time of William I (1165-1214), the mercat cross served as a official symbol of a town's right to serve as a center of trade, and merchants were to meet at the cross to do business. Possessing the mercat cross was, historically, a right granted by the monarch, or through the local bishop or baron. The cross1 indicated that the burgh had the right to hold a regular market and fair, and was used as a place to conduct business and make official decrees. Even in more modern times (up until the 1700s and beyond) the cross remained the marker for the town marketplace and was the traditional place for auctions to be held.
They were originally placed, as you might expect, in the market place, although in later days they were more likely to indicate a main square than a market. In many cases, on market days large weighing arms were attached to provide an official, standardized measuring system. Official announcements were made at the cross, and punishments were carried out there. Initially the cross was a simple post topped with a heraldic or religious emblem, but it slowly evolved to be more important as a central monument than as a symbol of the market, and many 'modern' crosses are not in the form of posts at all, but are stone crosses, pillars supporting statuary, or ornate gazebo-type structures.
In some towns official announcements are still made at the cross; the cross at Edinburgh2 is still used when royalty dies and for the calling of parliamentary general elections. In centuries past every announcement3 of import to the public was made at the local cross, from the announcement to kick off a fair to the punishment of criminals. If an announcement was made at the cross it was legally held to be common knowledge.
Punishment at the cross might be as mild as a requirement that one stand by the cross for a specified amount of time with a paper stating one's crime, or as severe as a hanging. There are many accounts of people being tied to the cross and having eggs thrown at them, stories of thieves having their ears nailed to the cross and having their victims come by to spit on them or empty chamber pots over them, and occasional cases of people being burned alive at the mercat cross.
English towns also had market crosses, which they did indeed call 'market crosses', as do some early Australian and Canadian cities.
1. I use the term 'cross' for shorthand here, which is common enough in modern writings. In older works it is most common to find the terms 'mercat cross', 'public cross', and 'market cross' written in full. This is because the term 'cross' by itself could be used in Scots to means a cairn on a hilltop, the hand on a clock, the 'tail' side of a coin, or as a verb meaning 'to approach'. And, of course, a cross in the sense we use it today. However, the phrases 'punished at the cross' and 'burnt at the cross' were used with the understanding that the cross was the mercat cross.
2. The Mercat Cross, Edinburgh is an impressive monument -- quite literally. It currently stands 4.25 meters tall (reduced from 6 meters in 1756), consisting of a high square base supporting a pillar topped by the Royal Unicorn.
3. In Scots the act of making an announcement at the cross was referred to as 'fencing' or 'crying'.
References and Further Reading:
Influence of the Pre-reformation Church on Scottish Place-names by James Murray Mackinlay, pub.
W. Blackwood, 1904; link.
Notices, Historical, Statistical and Biographical, Relating to the Parish of Carluke, from 1288 Till 1874 by W. Rankin, pub. Carluke 1874; link.
Wikipedia: Mercat Cross
NTS: On the Ayrshire Trail:
Exploring the Mercat Cross in Ayrshire
Wikipedia: Mercat Cross, Edinburgh
The Concise Scots Dictionary compiled by Alexander Warrack, pub. Crescent Books, 1988
The Oxford English Dictionary.