Aside from the title, the word "heart" first appears in the text in this line:
...the bond of the sea. Besides holding our hearts together through long periods of separation, it had the effect of making us tolerant of each other's yarns...
The use here is of a connection felt deeper than simply association. The people who live and work on the sea know each other because of their shared experiences, and are aware of their own unique issues and the need to tell stories -- true or untrue -- to deal with internal problems. This directly sets up Marlow's story.
Another example comes in the description of a man who had been beating a native worker:
'Not in bed yet,' he said, with a kind of servile heartiness...
Here, the word "heartiness" is used to indicate a false bravado; the beating is not necessarily warranted, and the man performing the brutal act switches his demeanor from enjoying the act to submissive in the presence of the Manager. He expected to have no oversight, and uses "servile heartiness" to avoid guilt or shame.
The title appears verbatim later in the text:
We penetrated deeper and deeper into the heart of darkness.
(Conrad, Heart of Darkness, eNotes eText)
This is both a reference to the deep parts of the jungle thought of as "darkest Africa" and to the madness that Marlow soon discovers in men who have spent too much time in it. The further into the jungle they travel, the more their mental states begin to unravel, with Kurtz's insanity as the inevitable conclusion.