People are far more likely to complete suicide with lethal means like a gun than in other ways. This is demonstrated in the differences in suicide rates between the sexes. Women are a little less than 3x more likely to ATTEMPT suicide, but men are a little over 3x more likely to COMPLETE suicide. One of the explanations for this difference is that men are far more likely to use lethal means when attempting.

Easy access to a firearm for a depressed person with suicidal thoughts dramatically increases the risk of suicide because it is often an in-the-moment decision. There are exceptions when it is a thought out plan, but most often it is an impulse, and the vast majority of those who survive the attempt express regret in the after moments (such as while falling, or trying to vomit the pills they just took). People who attempt suicide with a firearm rarely have that after moment. Consequently, states with easier access to firearms tend to have higher suicide rates.

Disclaimer: this is not a post blaming the gun for the suicide. I am aware that you are more likely to die by car accident when you drive. My point is exactly what I stated. Easier access to guns means easier access to suicide, and is ONE (not THE) of the explanatory variables for the maps on display.