When and where?

As others have said, the medieval period covers a huge amount of territory and a knight might use several different types of sword even in a fairly well defined time and place.

That said, there are some general statements which can be made.

The most common sword type for a medieval European knight (between say the eleventh and fifteenth centuries in Western Europe at least) was a straight, double-edged weapon made to be used in one hand. The hand would be protected by quillions at least and it would have a pommel. The blade tapered from a fairly wide base near the guard to a narrow point, making it well suited to thrusting, although it was also capable of cuts. This kind of sword is known in modern terminology as an 'arming sword' or 'knightly sword' but medieval people generally didn't distinguish them with a name other than their usual word for 'sword'. There are a lot of variants, with different lengths, blade geometry, hilts, etc. This is basically what people usually think of when they imagine a knight's sword.

Another common type was the cut-optimised backsword, usually slightly curved and only fully sharpened on one side. These were sometimes classed as 'knives' rather than 'swords' by medieval people, but most of them are much bigger than what modern people would call a knife. They could have hilts and guards like knightly swords, but sometimes lacked a proper guard and/or pommel. Size varied more than for the knightly sword, with some being quite small and others very large. The more tip-heavy ones were known as falchions. Although it's hard to generalise, backswords were overall slightly cheaper than double-edged thrusting swords and might have been more popular with a slightly lower social class, but there are plenty of depictions of knights using them.

In the late medieval period, swords got a bit more specialised. Arming swords evolved into civilian duelling weapons with longer and narrower blades, eventually turning into rapiers. Some people used larger swords, like longswords. Blunt-edged estocs were used to thrust into the gaps of plate armour. Guards became far more elaborate.

You need to be more specific because "the medieval age" is nearly a millennium in time, broadly defined and occurred across multiple continents. Knight can be a highly ambiguous term also.

You'll get an answer if you ask about, say, 12th century France but as written this is too broad.