In @SS-3's comment is perhaps another way to answer the question.
Edit: 1) Additional supporting material (re: Kylo Ren) from the novel was added to provide a more comprehensive illustration of the two-way 'action and reaction' between Kylo Ren and Leia. 2) Caps usage has been trimmed down.
1) Leia knows that Han is going to attempt to
'reach' their son.
This is a fact as this is something she specifically requests of Han before he leaves as she tells him to
"bring him home".
2) Those sensitive to the Force have the potential to sense others who are also sensitive to the Force... (or sense the deaths of many like with the destruction of Alderaan, for example).
This is a fact re-suggested in the movie when the Supreme Leader and Kylo Ren talk about sensing Rey who is sensitive to the Force and is awakening to it.
With these two ideas in mind, my answer is that
Force-sensitive Leia sensed the abomination that Kylo Ren - her own force-sensitive son - did, which was to kill his own father.
I believe this answer is potentially further supported by two particular instances in the book where:
1a) Kylo Ren reacts to the mention of his mother...
“No, it’s not.” Halfway across the walkway now, Han continued to move forward, smiling. “Never too late for the truth. Leave here with me. Come home.” Without the slightest trace of malice or deception, he cast a dagger. “Your mother misses you.”
A strange sensation touched the younger man’s cheeks. Something long forgotten. Dampness. Tears.
“I’m being torn apart. I want—I want to be free of this pain.”
1b) Kylo Ren reacts to what he's done...
Stunned by his own action, Kylo Ren fell to his knees. Following through on the act ought to have made him stronger, a part of him believed. Instead, he found himself weakened.
2) Leia admits that she knew of
their son's potential corruption by and to the Dark side since the beginning... and yet tried to deny it and hide it because 1) she didn't think Han would handle it too well, and 2) she wanted to believe that their son could be kept with the Light and either not turned or capable of redemption.
In this, Leia shows
denial - YEARS of denial - when in truth, she knew deep down and long ago what really was going on and was likely to happen.
Sending Han out to try and save their son reads, to me, like another last-ditch effort where she - once again - is 'naively' hoping for something that will likely not happen the way she wishes to.
Though we have no idea as of yet if
redemption is in the cards for Ben, killing his own father
is a pretty big deal and coupled with the fact that
Kylo Ren is shown to emotionally react to the mention of his mother (or just the sense of family)...
For Leia, I think that's more than enough of a 'disturbance' in the Force
(specifically, her son emotionally reacting towards the mention of her and family and being corrupted/turned enough to the Dark to kill his own father)
for her to sense and be aware of.
Note: Please excuse the choppy formatting of this answer as I am trying my best to ensure the majority of spoiler-worthy material is kept behind the spoiler tags while still keeping my answer readable.