The Ace of Hearts (A♥) is almost universally known as the house card. I do not know why this is the case. Since I recently talked about the Bolognese Tarot, I will note that the Ace of Cups (which correspond to Hearts) is called the House in that system, which goes back many centuries, even before Etteila (who, after all, admits to having learned from Italian card readers, although he ended up switching some cards around).

The way I have rationalized the Ace of Hearts in my system is that Hearts represent all things inner and intimate and aces have to do with beginnings. They are in a way the source of the theme they speak of. The source of our inner side, of our intimate side, is our family, our house, the place where we consider ourself “inside” rather than “outside”.

The Ace of Hearts is the card of the Querent’s house, and usually describes it in a neutral to slightly positive way. The house can be intended as the physical place of residence or as the group that inhabits it, thus signifying the querent’s family. A Court Card falling near the Ace of Hearts can show a family member (or, depending on the question, a person who wants to start a family with the querent).
However, if the Ace is attended by Spades, it shows a negative environment or tears at home. These can very well end up affecting other aspects of the querent’s life.

Broadly, the Ace of Hearts can show a positive beginning to anything, and something that is solid and stable or brings stability to the querent. It also shows serious intentions in all aspects of life. For instance, if a perspective business partner shows up with the Ace of Hearts next to him, it doesn’t necessarily mean he has the hots for the querent. It can simply mean he’s serious and dependable, solid.
Because the Ace of Hearts shows positive beginnings, it is auspicious for pregnancies.

Psychologically and spiritually, the Ace of Hearts is a card of protection, but more broadly it signifies the querent’s inner side, his intimate feelings and perceptions, which may be described by the surrounding cards. Thus, the card can shed light on the whys and wherefores of his behavior.
With Diamonds preceding it, the Ace of Hearts can show money being invested in the family or in the house. With Clubs it can point to family activities or plans, while with other Hearts it shows harmony in the house. Spades, as already said, bring strife in the family.

Some Combinations:

A♥ – 2♥ = family visits | broadly, it refers to relatives | it can signify the arrival of something positive
A♥ – 9♥ = traditionally it signifies greetings in the family, but more generally it shows a great joy about one’s intimate and family life
A♥ – 6♠ – Q♣ or K♣ = can mean an inherited desease or more generally catching an illness from a family member
A♥ – 3♣ = married life, a strong family bond
3♦ – A♥ – 5♦ = spending money on renovations