A "hot button" issue is any issue that generates a lot of passion among a significant portion of a specific population. Such an issue is one that is very much in the news, thus playing off the figurative meaning of the word "hot" as something that is current. Most "hot button" issues in modern times are ones that concern politicians trying to serve their constituents by tackling these problems. The phrase most likely evolved from the phrase "panic button" into the meaning that is accepted in today's culture.
Many words or phrases come to mean something far different that what their literal definitions might be. Such words or phrases are known as idioms, which manage to develop their meanings based not on their origins or their literal definitions but rather based on the way they are used in a specific culture. These idioms are often colorful and colloquial and can prevent speech from becoming too dull or stilted. One idiom pertaining to current events and issues in the news is the phrase "hot button."
Any issues that are described in this manner are ones that have a lot of people talking about them. In addition, such issues are generally expected to raise strong feelings and opinions from the people who are concerned with them. As a result, these issues tend to draw the attention of politicians who are running for office. For example, someone might say, "He made that hot button issue a major focus of his campaign and it helped him to get elected."
It is important to understand that issues described in this manner may start to lose their currency and, thus, might no longer deserve the description. In the typical cycle of news it is possible that an issue that grabs front page headlines one day may be relegated to the small print the next. When that occurs, a new issue is likely to take its place. As an example, consider the sentence, "Gun control is a hot button issue once again after the recent shootings that were in the news."
In this sense, the phrase gets its meaning from the fact that the word "hot" can imply that something is current or trendy. There may also be some relation to the phrase "panic button," although the different meanings of the two phrases make this connection tenuous at best. It is best to label something a "hot button" issue when it is both timely and important to a lot of people.