Basics of D&D
D&D runs off of what we call a "d20 System" which means that the 20-side die is the core of game system. The majority of the rolls you make in D&D will be done with a d20, with modifiers added to it for increased or decreased chance of success. For the most part, any time you roll dice for anything other than damage or healing, you're going to roll a d20.
Here are some terms for you to familiarize yourself with if you are new to D&D.
Initiative (d20): this mechanic determines the order of play during combat. The higher your initiative, the sooner you get to act. Initiative is a Dexterity check, so when you roll the d20 you add your Dexterity modifier to the result.
Attack (d20): Attack rolls are used for all forms of attacks (melee, ranged, and spell), to see if your attack successfully damages your target. When you make an attack roll with a weapon that you are proficient with, you add your Proficiency modifier to the roll (+2 for level 1 characters). You also add either your Strength modifier (melee weapons, optional for thrown weapons), your Dexterity modifier (ranged weapons, optional for thrown weapons, optional for melee weapons with the Finesse property), or the modifier for the spellcasting ability (Int for Wizards, Fighters and Rogues - Wis for Clerics and Druids - Charisma for Bards, Sorcerers and Warlocks). Rolling a natural 20 on an attack means that you automatically hit regardless of the target's armor class, and you deal increased damage.
If you are not proficient with a weapon, you still add modifies for the ability score, but you do not add your proficiency modifier.
Skill Checks (d20): Skill checks are used to have your character accomplish various tasks such as climbing, swimming, hiding, picking locks, crafting, applying a disguise, lying successfully, character knowledge, and so forth. When you are proficient with a skill (either from your race, class, background, or feats) you get to add your proficiency bonus to the d20 roll. In addition to that, you also add the modifier from whichever attribute is tied to that particular skill. Rolling a natural 20 on a skill check is an automatic success.
Ability Checks (d20): Ability checks are very similar to Skill checks, and work exactly the same way. Sometimes a particular skill is not quite right for an action that your character is performing, so rather than asking for a skill check, you will be asked for an Ability Check. In these cases, you will roll 1d20 and add the modifier for the ability in question. Rolling a natural 20 on an ability check is an automatic success.
Saving Throw (d20): Saving Throws are a form of active defense targeting different abilities (Str, Dex, Con, Int, Wis, or Cha). When you make an attack, you are doing active offense, meaning that you are making a roll to actively overcome the target's defenses (armor class) in order to succeed on the attack. Saving Throws are the same concept, just in reverse. So instead of trying to meet-or-beat the opposing defense, you are trying to meet-or-beat the incoming offense. These rolls will most often come in response to spells or traps. If you are proficient in a particular type of saving throw (determined by your class) then you add your proficiency bonus to the roll. All saving throws are tied to a specific ability (Str save, Dex save, etc), so you also add the corresponding ability modifier. Rolling a natural 20 on a saving throw is an automatic success.
Death Saving Throw (d20): Death saves are a special roll made when your character is at 0 HP and dying. Each round that you are at 0 HP, and not stabilized, you have to make a Death save. Death saves do not have any modifiers at all, you simply roll a d20. If the roll is 10 or higher, you succeed. Otherwise you fail. The goal with death saving throws is to roll 3 successes before you roll 3 failures, so best 3 out of 5. If you get 3 successes then you stabilize yourself and no longer have to make death saving throws. If you get 3 failures before you stabilize, then your character dies. Rolling a natural 20 on a death saving throw not only stabilizes you, it also restores you to 1 HP and brings you back to consciousness.