what is a eukaryote and what makes it different than a prokaryote?

the biggest difference is that eukaryotes have a nucleus and a cell wall. an easy way to remember this is to think that EUK rhymes with NUC.

eukaryote are cells with a definite nucleus.
prokaryote are cells without a definite nucleus. The nuclear matter is scattered within the cell with no nuclear membrane.
this is the difference.

A eukaryote is a type of cell, or organism comprised of eukaryotic cells.

The main difference is that a eukaryote has a membrane-bound nucleus and organelles, whereas a prokaryote has neither.

Eukaryotic cells have a nucleus (eukaryotic means 'having a true nucleus'). Prokaryotic cells don't. That is the basic difference.

Other differences are:
Prokaryotic cells are smaller.
Prokaryotic cells only have one membrane (the one around the outside). They have no membrane bound organelles.
Prokaryotic cells are surrounded by a cell wall but it is made of peptidoglycan not cellulose.
Prokaryotic cells contain ribosomes that are smaller than eukaryotic ribosomes.
Prokaryotic cells' DNA is in the cytoplasm in the form of a single loop called a 'circular chromosome' or 'bacterial chromosome'.
Many prokaryotic cells contain small DNA loops called plasmids.
Prokaryotic cells DNA is not surrounded by a membrane. The general area it is found in is called the nucleoid.
In prokaryotic cells ATP production takes place in specialised infolded regions of the cell surface membrane called mesosomes.
Some prokaryotic cells have a flagellum which function like eukaryotic undulipodia but have a different internal structure.

Hope this helped you!