I heard something from one of the candidates on election day:
I intend to address these challenges head-on.
What does this mean?
Specifically, I’m not sure what it means to address something head-on.
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This is the sense of “address” your quotation employs:
a : to direct the efforts or attention of (oneself)
[he] will address [. . .] the problem
b : to deal with : treat
[he was] intrigued by the chance to address important issues
Applying this to the rest of the quotation, we can say this candidate intends to direct his own efforts and/or attention to some aforementioned challenges in some way.
To learn how he’ll be dealing with these challenges, we need to know what he meant by “head-on”.
in a very direct way
Adding that together, we can say he is claiming he will attend to these challenges in a direct way; he won’t delay, delegate, or ignore these issues, but instead attack them with full focus and immediacy.
To "address (something) head on" means to take direct action to improve a situation. Politicians often use this phrase to mean that they are not hiding from difficult issues (challenges) and will take direct action on the matter.
This website has a nice detailed answer for that exact phrase: http://www.phrasemix.com/examples/i-intend-to-address-these-challenges-head-on