At best you'd get a sketch of the village and surrounding properties and roads leading to other settlements and locations. Most peasants -I'm assuming we're just talking simple farmers here- wouldn't travel much outside of their local area since their most valuable possession was the land they worked and long-distance travel just wasn't a factor in their daily lives, on top of being dangerous and difficult. life. Their world would consist of their immediate neighbours and family and their livelihood and precious few would have a significant grasp of much beyond that since it wasn't relevant.

Well, probably poorly. A lot of the world hadn't been discovered by Europeans at the time, even! I can't actually answer for how good they would have been at drawing maps although I have some nice saved images of maps (by monks, mainly) of the world, which shows how even some of the most knowledgeable people had many warped views of the world- including within their country.

I can answer for what a generic peasant or rural people (but not peasants) in Western Europe in the 1500s would have known about the world. Religion was an incredibly important part of people's lives- they'd have gone to church regularly, prayed regularly, richer people had Book of hours, wars were fought over religion, people died over religion. That isn't to say they knew the Bible inside out, probably only the most interesting parts, the colourful stories- of Moses, the birth and death of Jesus, the story of Paul, Noah, Abraham, Jonah, to name a few. Saints were also a popular and important part of daily life, and you would know them as 'Saint X of X'. People would pray to saints and they would know the stories and lives of some saints as a result. People might know of Saint Patrick and therefore knew that Ireland was across the sea and close to Britain, for example.

So, from Biblical and saintly sources, an average Medieval religious person could know of: Egypt (and they would know Egypt had desert and was at least someowhere near Israel, they would know the river Nile was in Egypt and therefore of the River Nile, for example ' Then Pharaoh’s daughter went down to the Nile to bathe,' Exodus 2:7, ). They would know it was possible to travel to Egypt from Israel/Palestine (due to the story of Jesus and his family fleeing there), they'd have known of Bethlehem, Gallilee, Jerusalem and vaguely of Nazareth. The story of Saul/Paul would have been relevant especially in times of often extreme anti semitism, as well as a moralistic story which for many could be inspiring. From that, they would have known of Damascus at the very least. They would have known of Jericho. They would have known of Mount Sinai and therefore have vaguely known that around Egypt, there were mountains, so a very basic physical geographical knowledge. From the exciting story of Jonah, they may have known of Nineveh but would probably have no idea of where it was in relation to the world, but assume it would be close to Israel and Egypt. Depending on the priest, their memory and how religious the peasant was, they may know in greater detail about the stories and therefore know about Mesopotamia and some basic geography, such as Ur. We can assume that although I doubt they could draw a map, but they would know of some basic physical geography of Egypt and the Near East (eg there were deserts, there were mountains, there was the Red Sea).

We also must look at wars. News and gossip spread fast in the 1500s, as gossip without the Internet does even today. And peasants did fight in those wars, they would come home and tell about their experiences. Peasants would sometimes go on pilgrimages- whether to local places of worship or on longer pilgrimages. They might have met foreigners on those pilgrimages even. Stories from outside their region may well have been told- the Aenid was a popular story for example.

So- I doubt they could draw a map of the world. They might think 'well, Canterbury is to the west of me, where there is also Rochester, and Dover is South East from me. London is on the same road as Rochester and Canterbury and is further north. Taxes were raised so we could go to war with France and some people fought in France and they went to Dover and crossed to the East from there, so France is across the sea to the East, but I don't know how far. Also, there were wars with Scotland which is somewhere up North, and I knew someone who said they knew someone who went through York to go up to fight, so York is up North and Scotland is more northernly than that. And I also heard about this massive rebellion in Norfolk and apparently they went to London and that Then they might say 'I know that Egypt is next to Israel and near the border there's some mountains. In Israel, there's Jerusalem, near Jerusalem there's Nazareth and Bethlehem. There's also a sea on the border of Israel.'

Some poor people may have gone to plays, as groundlings. From there, they could learn about the many international places the plays often involved. They would not be a peasant, but a poor Londoner could know about Venice, Rome, Verona, just to name a few. They may not have been able to draw a map of Italy, but they could name a few major cities or towns in Italy. The stories would have spread from the towns and cities to rural areas gradually, so poorer risk workers would also have known some basic world geography from entertainment.