I have learned that there are white holes and black holes in the universe, but I am confused as to what a wormhole is. Is it a tunnel that connects black and white holes?
A wormhole is, in theory, a 'tunnel' which would be a shortcut to another point in spacetime. There's a Wikipedia article on the subject:
A wormhole, also known as an Einstein–Rosen bridge, is a hypothetical topological feature of spacetime that would be, fundamentally, a "shortcut" through spacetime. For a simple visual explanation of a wormhole, consider spacetime visualized as a two-dimensional (2D) surface. If this surface is folded along a third dimension, it allows one to picture a wormhole "bridge".
If you're the physicsy type, this might make some sense to you:
If a Minkowski spacetime contains a compact region Ω, and if the topology of Ω is of the form
Ω ~ R x Σ
where Σ is a three-manifold of the nontrivial topology, whose boundary has topology of the form
∂Σ ~ S2,
and if, furthermore, the hypersurfaces Σ are all spacelike, then the region Ω contains a quasipermanent intra-universe wormhole.
If this makes absolutely no sense to you, then you are just like me. Congratulations! For those that don't speak Greek math (such as me), here's an English explanation from space.com:
A wormhole is a theoretical passage through space-time that could create shortcuts for long journeys across the universe. Wormholes are predicted by the theory of general relativity. But be wary: wormholes bring with them the dangers of sudden collapse, high radiation and dangerous contact with exotic matter.
And here's a pretty picture of the effect:
A model of 'folded' space-time illustrates how a wormhole bridge might form with at least two mouths that are connected to a single throat or tube.
In plain English, it's a shortcut through spacetime, and the primary conceivable way time travel could happen.
A wormhole is a theorised phenomenon that would, if they exist, connect two different parts of space-time. A common analogy for the wormhole is to represent space-time as a two-dimensional sheet. If the two-dimensional sheet is bended over so that two points touch each other, than the point of contact becomes a wormhole. This has been suggested as a way to effectively travel faster than the speed of light (without actually travelling faster than the speed of light). As with most things, there are different theories about how a wormhole could exist and what its properties would be.
I have learned that there are white holes and black holes in the universe,
Our universe has black holes. It doesn't have white holes. A white hole can't form through gravitational collapse from realistic initial conditions, assuming realistic forms of matter.
For similar reasons, it is extremely unlikely that wormholes exist in our universe or can be formed through any realistic physical process.
but I am confused as to what a wormhole is. Is it a tunnel that connects black and white holes?
No, it isn't.
There are actually various different types of wormholes that are consistent with what we know about general relativity. They can be traversible or nontraversible.
One of the earliest wormhole solutions to be studied was one that occurs in a mathematically idealized spacetime containing a black hole, a white hole, and two separate copies of the external universe. This is called the maximal extension of the Schwarzschild spacetime. It can't be a realistic model of our universe or of anything that could form in our universe. In this spacetime, there is a non-traversible wormhole connecting the two copies of the external universe. These regions are labeled regions I and III. You can't get from I to III without passing through the black hole or the white hole (regions II and IV), which means you can't get from I to III without going faster than the speed of light. I.e., it's impossible. This is why it's non-traversible.
A traversible wormhole would be one that would allow you to pass from one region to another. These could be either two regions in the same spacetime or two completely separate universes. It would not have event horizons like those of a black hole or white hole, because if it did, it wouldn't be traversible.