While traveling with Ivy, her affinity for you might slowly rise if you treat her well. Ivy does not judge your behavior in the Commonwealth. Instead she will judge you solely on how you treat her as individual. As Ivy's affinity rises, with each jump, hundreds of new lines of dialogue become available. Ivy will react to both dialogue and many different types of actions differently, depending on her affinity for you. 

Among other things, Ivy's affinity can rise by talking to her, sleeping with her and taking her to nice places. The more attention you give Ivy, the quicker her affinity for you will rise. As affinity rises, quests will be initiated that reveal more about her past. These quests can include new cells and unvisited locations...

There are more reasons why Ivy is called a Prime Companion. All of her dialogue is rooted in a diverse set of emotions, including among other things fear, arousal, irritation, love and anger. During dialogue with Ivy, or after certain player actions, she will convey these emotions to the player. If a high enough level of love is reached, Ivy will propose her love and a deeper emotional relationship will become a possibility. Only after establishing a loving relationship with Ivy, one that goes beyond mere friendship, will she divulge her deepest secrets. Just like any relationship in real life, relationships can end.. and there is a maximum to how often Ivy will want to re-establish a relationship with the player.

Affinity will continue rise long after a relationship with Ivy has been established so that as you continue to play with Ivy, you will see her 'learn' and 'grow' as an individual, while you travel with her and speak with her.

It is possible to irritate Ivy to such an extent that she will become angry with the player. In this case she will not engage in sexual talk and some of her functions will be disabled. 

If Ivy reaches such a state, players can remedy the situation by speaking to Ivy and attempting to apologize. Besides apologizing, showing Ivy that you care about her, by finishing quests for her, listening to her and being kind to her, will slowly lower her irritation levels to a point where an apology will be easier to attempt. Once her irritation levels are low enough, all functions will be re-enabled.