Euclid's Elements has 13 books. Book 1 starts with definitions.
Here are the first few:
1. A point is that which has no part.
2. A line is a breadthless length.
3. The extremities of a line are points.
4. A straight line is a line which lies evenly with the points on itself.
5. A surface is that which has length and breadth only.
The main problem is that modern language and his language are a bit confusing. We don't use "extremities".
The definition of straight line above might not be clear unless you already know what a straight line is.
But in total, Euclid defines: point, line, straight line, surface, plane, plane angle, right angle, perpendicular angle, obtuse angle, acute angle, boundary, figure, circle, center, diameter, semicircle, equilateral triangle, isosceles triangle, scalene triangle, square, rhombus, trapezoid, parallel.
The 5 postulates are (in his words)
1. [One can] draw a straight line from any point to any point
2. [One can] produce a finite straight line continuously in a straight line.
3. [One can] describe a circle with any center and distance.
4. All right angles are equal to one another.
5. If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, athe two straight lines, if produce indefinitely, meet on that side on which are the angles less than the two right angles.
In modern terminology, we usually list the first postulate as "two points determine a line". The fifth one is often rewritten to say "parallel lines don't intersect"; it's the most famous for being the one that makes the geometry described here planar--remove that postulate, and look at the lines of longitude on the globe.
So why are these postulates not definitions? The fifth one is complicated enough to be phrased as an "if-then", so it's probably reasonably clear why that's not a definition.
But why do we need to postulate a line or a circle, rather than define it?
Postulating a circle means we postulate its existence. We could just define a circle or a line, but it doesn't mean that such a thing with those properties as defined exists.
And we can't prove that those things exist, either. We have to assume them. This may be the oddest thing to a young student. "WHAT do you MEAN a circle doesn't EXIST? Look, I can draw one." (The standard answer to this is that any drawn circle is actually imperfect--doesn't have constant radius, doesn't have a boundary of no thickness, etc. This is typically a deeply unsatisfying answer. You could then tell him about the REAL constructivists: mathematicians who tried to construct all of math using the actual constructed "non platonic" geometry they could realize...but that's for another day.)
But this is where constructions come from, and this is what they were for. The answer to the above complaint is that you can actually CONSTRUCT everything you're asked to prove using just three things: a straight edge, a compass, and a pencil.
That is what it means to say "postulate a circle": it means "give yourself a compass to create a circle out of thin air." Same with "postulate a line: "give yourself a straight edge", and "postulate a line segment" : "give yourself a pencil to mark points on your line.
Then, the postulates have real meanings, because you can create everything else from those devices. Equilateral triangles are defined, but their existence is proved--and can be proved by construction from just the above three tools. Same with regular polygons, various congruent angles and lines, etc.
The idea that you start with 24 postulates is really really depressing, since it undermines everything beautiful about geometry that could be seen by construction.
Here's a link to Euclid's books. It contains all of the propositions and hyperlinks to the proofs.
Sometimes it's difficult to see the great truth he proved geometrically because of his wording and naming conventions. (Would you recognize his proof of the factoring of (x^2 -1) ?) But reading this might show you what you need to know and what's superfluous. And it will show you how to prove 19 of those postulates...