A transitional fossil is any fossil which gives us information about a transition from one species to another. (Or, about a transition from one group of species to another group of species.) A transition simply means that, down through time, there was some sort of change. The change must be big enough so that each non-transitional fossil can be easily be sorted into either a "before the transition" pile, or a "after the transition" pile. A transitional fossil is one that falls between the two piles.
Suppose some species A was unchanged for 2,000,000 years. Then, across 200,000 years, they became smaller and acquired wider feet. After the change, we think of them as species B, and they remain unchanged for another 2,000,000 years. Then any fossil from that 200,000-year period of transition is a transitional fossil.
In this example, you would expect every transitional fossil to predate every fossil from species B. However, it is not true that the transitional fossils must be more recent than all species-A fossils. This is because the transition can happen to an isolated group of A's, instead of to all A's. (In other words: the existence of a child doesn't mean the parent vanished.) In fact, there are examples where a parent species is alive to this day.
The transitional fossil is interesting because it tells us details of how the change happened. In this example, it could be that the creatures first became small, and then later got big feet. Or it could be the other way around. Or, the two trends could have been simultaneous: the features could have co-evolved. A nice transitional fossil tells which of these three possibilities is the one that actually happened.
If speciations can occur, then a series of them can occur.
Assume that species A gave rise to species B, who gave rise to C, etc etc, until finally species Z emerged. Let's also assume that we only have fossils from A and Z. Then, one day, we find a fossil that falls in between A and Z.
This new fossil isn't necessarily from a time of transition. It could be from a species which was stable for a long, long time. However, if the fossil looks in-between A and Z, and is of the right age (etc etc), then we might as well call it transitional.
Notice that this is a question of viewpoint. This kind of fossil is only transitional because we are talking about its relationship to A and Z.
It gets worse. A species can fork, and become several species. (Suppose the ocean rises, and breaks their territory into many islands.) So instead of the family tree being a simple linear chain such as
A ===> transitional ===> Zinstead we might have
A ===|===> B
|
|===> C
|
|===> D ===|===> E
|
|===> F ===|===> H
|
|===> J ===> Z
In this example family tree, A was the "parent" of three species B, C and D. D was the "parent" of E and F, and so on. The path of descent from A to Z is A-D-F-J-Z.
Now, suppose we find a fossil from species B, C, E or H. These are off the path of descent. But, they may teach us something about the sequence of events down the path of descent. If they do, then they are transitional in a broad sense, although they aren't transitional in the narrowest sense.
So, the real complication is that there are now shades of gray, as discussed in this infamous quote.
Assume that A is a group of very similar species, so that all their fossils would clearly belong into the group. (Fossils are often incomplete, so it sometimes happens that we know a fossil's group, but don't know exactly which member of the group.)
Later, there was another group, B, and the two groups seem related. The Darwinian explanation would be that the B's are so similar because one species gave rise to them all. And, that founder species was descended from some member of the A group.
Any fossil which falls between the groups is by definition transitional. The complication is that there are shades of gray. As with the chain example above, there can be species which are side branches off the chain of descent. To be more precise, there is a path through the family tree that leads to the B group, and with 20/20 hindsight we identify that path as a chain of descent. We can meaningfully talk about how "close" a species was to that chain. It's a little like talking about cousins, second cousins, and such.
Obviously, we would always prefer to have fossils which were unambiguously transitional in the strict sense. Some fossils are. Some are clearly only transitional in the broader sense. And, sadly, sometimes we aren't sure, and we will stay unsure until further fossils turn up.
If two groups of creatures are similar, then a transitional creature would have looked like something part-way between.
If the two groups of creatures are very far apart in time, then it gets more interesting. There could be many ways to get from A to Z, and we have imperfect knowledge of past environments.
For example, is there something transitional between walking and flying? One possible answer is "gliding". Another answer gives scenarios where a two-legged pursuer crosses gullies faster because its jumps are assisted by small wings. The most popular scenario for the evolution of insect flight is something else entirely. Paleontologists think that true flight evolved five times, and no single scenario fits all five cases.
According to Theory of Evolution, it was just another creature. Only someone with a time machine could tell what was to come. By definition, a group of transitionals left descendants. This means that in each and every generation, some of them lived well enough to have children. It is a prediction of the Theory of Evolution that the group was viable at every point in time. (And therefore, Evolution must explain, in each and every case, how that could be.)
Some Creationists assume divine intervention in transitions. This can be invoked to solve any problem that a transitional creature might have.
Other Creationists assume that each species gets destroyed, and then its successor species is an independent creation. These theories do not need to explain how an intermediate could be viable, since there are no intermediates. On the other hand, these theories cannot explain the intermediates that are in fact found.
No. The fossil is what a statistician would call a sample. It was a member of a group, and we are using it to learn about the group. The fossil of an immature creature is usually as educational to us as the fossil of an adult.
Basically, anything which teaches us about a transition is "transitional".
Some parts of the fossil record are good, in the sense that they provide a large number of well-preserved fossils, nicely spread out across spans of time. Transitional fossils are often found in those rockbeds. When fossils are rare, transitional fossils are also rare.
It is interesting to ask if good fossil records ever show a lack of transitional fossils. The answer is yes. However, there are known examples where a transition occurred in a specific geographic area. The new species then spread from that area, and arrived "suddenly" in other areas. If you dig in the wrong place, there are no transitionals. If you dig in the right place, there are.