Your fighter talks with the tavern keep, trying to pry out of her any information she may have about a number of unsettling rumors that have been circulating recently about the local ruling family. Are you successful? The DM could make a determination based on your roleplaying ability. On the other hand, knowing that while you have a great personality, your character has a Charisma score of 9, the DM could instead ask you to roll a Charisma (Persuasion) check. Although it's easy and often fun for DMs to rely solely on the creativity and quality of role-playing, 5e also provides a nice variety of skills (and a few plain ability checks) that apply to specific types of social interactions. They are spread out amongst the different abilities. I gather some of them together here in one place to make their use easier. I encourage you to use them -- this will more accurately reflect the social effectiveness of characters and be more fair to those players who invest in Charisma or allocate their precious skill allotment to one or more of these social interaction skills.
Skills and Simple Ability Checks. The Charisma (Persuasion) check, the Charisma (Intimidation) check, the Wisdom (Insight) check, the Charisma (Deception) check, and in certain circumstances the Charisma (Performance) check would be applicable in social interactions. (PHB pp. 175, 178, 179.)
Your chance of success with ability checks related to social interactions can be enhanced or reduced in a variety of ways. Sometimes two or more characters or creatures team up to attempt a task. In combat, this requires the Help action. If the DM determines the assistance helps in a social interaction, then the ability check (if there is one) is made with advantage. (PHB pp. 175, 192; DMG p. 245.)
Certain conditions give you advantage or disadvantage on an ability check. Examples include: A character that has charmed a creature has advantage on any ability check to interact socially with the creature that is charmed. A creature who is poisoned or exhausted (level 1) has disadvantage on ability checks. A frightened creature has disadvantage on ability checks while the source of its fear is within its line of sight. (PHB p. 290.) The target of Enhance Ability has for the duration of the spell advantage on certain ability checks: with Eagle’s Splendor the target has advantage on Charisma checks. (PHB p. 237.)
Magic Items. Certain magic items help you make an ability check by increasing one of your ability scores or giving you advantage on ability checks. A few magic items provide a bonus to ability checks or saving throws or both. For example, while a Stone of Good Luck is on your person, you gain a +1 bonus to ability checks and saving throws. (DMG p. 205.)
A feature of your class may affect your ability check rolls related to social interactions. For example: A bard can use Bardic Inspiration to "inspire others through stirring words or music." The recipient "gains one Bardic Inspiration die, a d6" and "can roll the die and add the number rolled to one ability check, attack roll, or saving throw it makes." (PHB p. 53.) With Peerless Skill the bard can add the Bardic Inspiration die to his or her own ability check. (PHB p. 55.) A rogue's use of Reliable Talent enables the rogue to add his or her proficiency bonus to any ability check and treat a d20 roll of 9 or lower as a 10. (PHB p. 96.)
Use Roleplaying and Ability Checks. Even if a DM calls for an ability check in social interaction situations, the DM could still rely on roleplaying to a degree. You don't want to discourage creativity and roleplaying. "Many DMs find that using a combination of the two approaches works best. By balancing the use of dice against deciding on success, you can encourage your players to strike a balance between relying on their bonuses and abilities and paying attention to the game and immersing themselves in its world." (DMG p. 236.) For example, one way to use both is when a DM allows roleplaying to guide the social interaction up to a certain point, and then calls for an ability check at a crucial juncture.