This is going to be a long answer: it recalls at the beginning the basic rules for the "action economy" in combat, then provides some examples and finally tries to clarify the case at hand.
Common rules for combat
The combat is divided in rounds, where the participants take turns following the initiative order.
Each participant, during a round, may do 4 things, which have specific names:
Normally, each option of the above list can be chosen only once per round1, in any order. You can see such list as your "portfolio" of 4 "slots" that you can spend in a round: once you spent an "Action slot", you cannot use another one until your next turn. Beside these 4 "slots", you can also do other things that do not "cost" anything: check the section Other Activity on Your Turn.
Each element of the above list is actually a set of options: let's focus on Actions.
The basic options for Action are Attack, Cast a Spell, Dash, Disengage, Dodge, Help, Hide, Ready, Search, Use an Object: when a participant is taking an action (or using an action) means that they are spending the "Action slot" and choosing one among those options. These are some of the choices, not all: there are other things that can be done spending an Action.
Monsters in combat
Before considering the case in the question, let's spend some words about how monsters can use their "portfolio" in combat.
Even monsters follow the same rules, i.e. they have the same 4 "slots" to spend in a round, and moreover their stat blocks present further options with the relative rules. For example, the Goblin Boss has the following ability:
Nimble Escape. The goblin can take the Disengage or Hide action as a bonus action on each of its turns.
This means that a Goblin Boss can spend its "Bonus Action slot" for taking the Hide action or Disengage action: for example, during their turn, they use their Action to Disengage from an enemy in melee combat, use their Movement to move away (without provoking opportunity attacks thanks to disengaging) and then use their Bonus Action to Hide.
Under the "Action" list of the Goblin Boss, one can read:
Multiattack. The goblin makes two attacks with its scimitar. The second attack has disadvantage.
This means that this monster can spend their Action to take the Multiattack action, i.e. choose as option for the "Action slot" of their portfolio the option Multiattack.
Finally, the Goblin Boss has also a personalized choice for the Reaction:
Redirect Attack. When a creature the goblin can see targets it with an attack, the goblin chooses another goblin within 5 feet of it. The two goblins swap places, and the chosen goblin becomes the target instead.
This means that beside the other options available for a Reaction, the Goblin can spend their "Reaction slot" of their portfolio and use the above ability.
Finally, your case
First of all, note that the Burrowing Worm ability of the Spawn of Kyuss costs an Action: this means that when using their Action (spending their "Action slot") the Spawn has to choose the Burrowing Worm ability or the Multiattack, they cannot use both of them in the same turn.
The description of Burrowing Worm reports (emphases mine):
The worm is a Tiny undead with AC 6, 1 hit point, a 2 (−4) in every ability score, and a speed of 1 foot. While on the target’s skin, the worm can be killed by normal means or scraped off using an action.
This means that a creature affected by such worm that wants to get rid off of the parasite has the following options:
- They can spend their Action to attack the worm: Attack is one of the option for the "action slot".
- They can spend their Action to scrap it off: hence the "Action slot" is spent and they cannot use it for hiding or disengaging, for example.
Consider now the barbarian: at 5th level they have the Extra Attack feature:
Beginning at 5th level, you can attack twice, instead of once, whenever you take the Attack action on your turn.
This means that a Barbarian can attack twice if they spend their "Action slot" for the Attack option. In the case at hand, since the description of the Burrowing worm says that it "can be killed by normal means", the Barbarian could have spent their Action slot to attack the worm, and then, due to the Extra Attack feature, they have still a further attack.
Note that if the Barbarian decide to use their Action slot to scrap off the worm, because they are using the Action slot to take the "scrap off" action and not the Attack action.
1 There are special game feature that allow to overrule this, for example fighter's Action Surge ability.