What does the bible mean when it refers to the 'heart'?

In both the Old Testament and the New Testament the word "heart" is used to refer to the whole of the innermost part of the human. This inner aspect of a man is made of three parts,

The mental process, which is the major part (where action & reaction take place), which is to lead a person in their life.
The emotions (which only process as reaction), are as enhancement to enrich our lives.
The will, (discretionary, volitional, decision-making) where decisions are made between the rational and the emotive.

So, in biblical terms the heart can be used as a general identifier of things pertaining to the heart, the mind, and the soul. All three parts are unique, but they can also be used interchangeably. The easiest way to think of these parts are in a Venn diagram where the heart and mind are two circles that overlap. The part that overlaps can be seen as the entire character of the person, referred to as the soul.

So, when speaking of the place where belief occurs, the New Testament authors can speak of the heart (Mark 11:23; 16:14; Luke 8:12; Rom 10:9) or the mind (Rom 12:2; 2 Cor 4:4) or even the soul (Acts 14:22 seems to fit in this regard).

Peter describes the inner man as "the hidden man of the heart" (1 Peter 3:4), or the "inner self" (other translations). It is the center of one's being (Proverbs 4:23), where he believes and exercises faith (Luke 24:25; Romans 10:9,10). It is the location of the human deliberation, where wisdom is employed. Understanding is said to be the function of the mind (Job 38:36), yet the connection to the heart is undeniable. The heart is where a person discerns the difference between right and wrong (1 Kings 3:9).

The heart is connected with thinking: As a person "thinketh in his heart, so is he" (Prov. 23:7). To ponder something in one's heart means to consider it carefully (Luke 1:66; 2:19). "To set one's heart on" is the literal Hebrew that means to give attention to something, to worry about it (1 Sam. 9:20). To call to heart (mind) something means to remember something (Isa. 46:8). All of these are functions of the mind, but are connected with the heart in biblical language.

Closely related to the mind are acts of the will, acts resulting from a conscious or even a deliberate decision. Thus, 2 Corinthians 9:7: "Every man according as he purposeth in his heart, so let him give." Ananias contrived his deed of lying to the Holy Spirit in his heart (Acts 5:4).

Not only is the heart associated with the activities of the mind and the will, but it is also closely connected to the feelings and affections of a person. Emotions such as joy originate in the heart (Ps. 4:7; Isa 65:14). Other emotions are ascribed to the heart, especially in the Old Testament. Nabal's fear is described by the phrase: "his heart died within him" (1 Sam. 25:37; compare Ps. 143:4). Discouragement or despair is described by the phrase "heaviness in the heart" which makes it stoop (Prov. 12:25).

The Heart and Mind Are Both Needed for Biblical Faith

We are saved through faith (Ephesians 2:8-10). The mind and heart must both be engaged in this process because to have faith in God, we must believe and trust God. Believing requires the mind, but to trust someone requires the heart.

The Heart and Mind Work Together in Our Relationship With God

To have an intimate relationship with God, you will have to engage your heart. To have a true relationship with God, you will have to engage your mind. You can passionately worship a false version of God, and you can lifelessly believe in a doctrinally accurate picture of God. God desires us to love him passionately and truly.

Philippians 4:4-7 Rejoice in the Lord always; again I will say, rejoice. 5 Let your reasonableness be known to everyone. The Lord is at hand; 6 do not be anxious about anything, but in everything by prayer and supplication with thanksgiving let your requests be made known to God. 7 And the peace of God, which surpasses all understanding, will guard your hearts and your minds in Christ Jesus."

This is a passage about our relationship with God. We must rejoice (an emotion of the heart) because God is near (an intellectual fact). We must be reasonable (mind). We must not be anxious (heart). We must pray about specific things in specific ways (which will require the mind). And when we do this, a peace that surpasses understanding will rest on us (which will be a feeling in the heart). Overall, when we have a relationship with God, the Bible says Christ Jesus will affect our heart and mind.

There are even more parts to a person other than the heart, the mind and the soul. What about the spirit of man? What about external influences that can affect the heart or the mind? For further definition of all of these, have a look at this article and form your own understanding of these parts of the whole.

Source: thebigpictureask.blogspot.com
This post also references information from the following sites:
applygodsword.com, faithalone.org, faithbibleministriesblog.com, and getbibleanswers.org