Good question! I see you are in one of my classes. For your information, the story I gave you in class is based on a real case Browne v. City of Grand Junction. I edited the title of your post slightly to give the actual case name.
1. The question the court asked is whether the law is constitutional or not.
Think about any test you had in school. If the teacher wanted all students to get a good grade he could make the test easy. If the teacher wanted to make grades lower he could give a hard test.
Strict scrutiny is a hard test. It usually makes the government fail.
Why a hard test? Well, if a law does one of the following things courts give the government a hard test:
a. the law discriminates against people because of race or religion.
b. the law allows some time of speech but prohibits other types of speech.
You could say that the court wants to make it hard for the law to be constitutional when the court applies strict scrutiny. In the case we discussed, the law allowed people to talk about politics and religion but did not allow people to ask for money. Because the law did not allow only certain kinds of speech, the court wanted to make it difficult for the government to win.
2. Here is another example.
Let's say a law provides that no one can give a speech in a public park after 10 p.m. That law does not distinguish between different kinds of speech. The law is just saying let's let people sleep after 10 p.m. People can make their speeches during the daytime.
But let's say the law says no one can criticize the government in a public park. However, people can talk about anything else. This law distinguishes between different kinds of speech. For that reason, courts want to give the government a difficult test. The government will have to pass the very difficult test of strict scrutiny to prove that the law is constitutional.