"Desperate" is an adjective that one most commonly uses when a person has to do a thing but does not have much hope of success. Thus feeling desperate might cause a person to do things they would not normally do.
It can also simply refer a very bad situation or a personal need.
For the first example I will use a woman named Maria. She always obeys all the traffic laws, but while visiting a friend one morning she remembers that she has forgotten an important business meeting. So we might write the following:
Maria drove her car at twice the speed limit because she was desperate to get to the meeting on time.
Maria wants very much to get to get to the meeting on time (perhaps the meeting is about her receiving a big promotion), so she does something she would not normally do (that is, break the posted speed limit on the road). She does this because she feels desperate.
Example Two (situation):
The second example refers to a situation where crowds of hungry people are fighting over food during a food shortage.
The famine has made for a desperate situation.
Here the overall circumstances seem hopeless. People who are otherwise kind and caring end up fighting over food because they believe their very survival is at stake.
I am desperate for a cold glass of water. (used when the speaker is extremely thirsty)
It is dangerous when the police corner a desperate thief. (this implies the thief might do something dangerous or unpredictable in order to avoid being captured)
So again, the word "desperate" usually conveys some sense of hopelessness and often causes people to act in ways they would not normally act.
I hope that helps!