Bit confused as to what they are, how you get them, and how they can be used.  Googling has only increased my confusion as there seems to be different sets of rules between editions, etc.

In combat, you can take one action, one bonus action, and move.  These do not need to be done in a specific order. A bonus action is going to be anything described as a “bonus action” in its text or spell timing - for example, Hunter’s Mark, the Ranger spell, lists Bonus Action as its casting time.

So, to provide an example a Ranger could cast hunters mark using their bonus action, then use their regular action to make an attack.

As a note, each edition of D&D is very different from one another - you cannot easily look at rules from one edition and try and extrapolate information about a different edition. 

Bonus actions can be thought of as "quick things."

Look at Rogue's Cunning Action for example. A rogue can hide, disengage, or dash as a bonus action.

Normally these are actions.

You get both an action and a bonus action on your turn. Attacking is a action most of the time. So the benefit for a rogue is that they can dash in and still attack. Whereas a non-rogue is going to have to choose to use their action either to dash or to attack, not both.

Depending on what in particular you're looking to do, there can also be additional rules.

For example when using two-weapon fighting you can (for example) use your action to attack with a dagger and your bonus action to attack with a second dagger. But your bonus action attack won't have additional damage from STR/DEX, just the base 1d4 of a dagger.

Or when casting a bonus action spell you're limiting on what spells, if any, you cast with your action to being only a cantrip.

Are there any specific things you've come across that you have questions on? That may be more effective than trying to get a general topic of bonus actions.

During a single Round, you usually get a single turn and a reaction.   A single turn usually includes a Move, an Action, and possibly a Bonus Action.  Bonus actions are limited - they cannot just be another regular action. Typical things that can be done as a bonus action are using Two Weapon Fighting, class abilities, and spells that cost you a bonus action rather than a turn.  What you can do with the Bonus Action depends on the particular abilties/spells, etc.

Note, there are certain common exceptions to this - such as Fighter's Action Surge, the spell Haste, and  the Rogue subclass Thief Ability Thieves Reflexes.

Legendary Monsters make it even more complicated with Legendary Actions, Lair Actions, Regional Effects, and other such complications.

The Basic Rules (which you can access here for free) breaks this stuff down in the rules' language in the Combat chapter's section on "Your Turn", Bonus actions (which are different from reactions and actions) are the first subheading in the Turn section:

https://www.dndbeyond.com/sources/basic-rules/combat#YourTurn

Especially given the state of D&D internet these days, I'd always start with this Basic Rules document for clarification rather than googling for a rule explanation.  The rules writing is actually pretty succinct and misinterpretations or imprecise explanations abound in Google Searches.

No.  We are experimenting with an after school club.  I myself haven't played in years and years and a lot of the rules have changed.  I've been watching/listening to Critical Role and Dimension 20 to try and jump start my knowledge and bonus actions were coming up a lot.  

Thanks for the information, everyone.  It helps.

I'm hesitant to add to the chorus because I tend to find that the more people who chime in, the more confusing the topic actually gets - more is not necessarily more. However, while this won't explain what's happening, it's a good way of understanding how Bonus Actions work.

Most things you'll do, will be a normal Action. Unless something tells you explicitly that it's a Bonus Action, then it's not (most likely an Action). There are comparatively few things you can do with a Bonus Action, and don't be surprised if most of the time, you end up not being able to use your Bonus Action. That is not a sign by any means that you're doing it wrong. There are certain builds that let you use your Bonus Action a lot (eg Rogues, casters to a lesser extent), but a lot of the time it'll be unused with other characters. Not all the time, but certainly enough to say that "Huh, I haven't used my Bonus Action yet, I must be doing something wrong" is incorrect.

Definitely distribute those free rules I linked above to the club, it's arguably what they're there for, and there are some folks out there in education research that believe engaging rules structures as found in TTRPGs like D&D help reinforce or lay the ground work for logic and reasoning skills (beyond the often SEL and reading literacy boosts that get promoted frequently in these discussions).  Like maybe a kid isn't up for writing a thesis on the narrator of "Sitting in the Catbird's Seat" but they're totally down for presenting a defense of why their rogue should only take at most a quarter maybe even 0 damage from the most recent fireball to hit the party.  

It's important to note an action and bonus action are not interchangeable. You can't for example, trade your action down to use a bonus action. They are completely separate pools of things you can do.

MidnightPlat, oh, the big selling point was the social/emotional benefits.

Definitely read at least the basic rules. I hadn't played since 2nd edition. The first time a Critical Role member asked to roll Stealth and Matt said to roll a d20 I was equally confused. I went out and bought the PHB just so I'd understand what was going on. 

Rathkryn, I've got the core soure books, plus two basic starter sets.  We've got an Educator's/After School Club account.  We're learning as we go.  I feel mostly comfortable, but there's still a few rough spots.