This topic is covered unusually well by other sites, but I'll cover it here, briefly.
If things are too predictable, players can simply solve your game. That's no fun. Things should be somewhat uncertain.
A good designer adds uncertainty, by using interlinking, and adding interaction between components or players. This makes the game too strategically complex for the players to solve. A player is not entirely certain what they should do, so they need to think about it.
A bad designer just throws in randomness, to create the uncertainty. It does the job, but with a host of downsides — it's often feelbad, disruptive, and anti-meritocratic.
You want players to have some ability to deduce or reason what's going to happen.
I've seen several very weak games, where players simultaneously choose an action, and then reveal it, to see what happens. In some of these games, the game system isn't complex enough to allow any kind of deduction, and the game just devolves into scissors-paper-rock, or reverse-reverse-reverse psychology madness, and you're interacting with an opponent who is also completely uncertain. Systems that are effectively random, are the worst kind of random.
Input randomness gives people randomness, but then lets them do something with it. The most common kind is simply drawing cards. You get random cards, but then you get to use them as you wish, and they have their non-random effect.
Output randomness means that you make your choice, and then the randomness occurs. This interferes with your plans, and there's nothing you can do about this kind of randomness.
In Monopoly, a player draws a card, and something happens immediately. There is no strategy, just random surprise.
In many games, players reveal a card from an "event deck" each round. This card can randomly harm some players, because no one could possibly have prepared for it.
Give the player time between when the random event occurs, and when it impacts the game. This allows the player to strategise, and do meaningful things.
You can use output randomness, but try to remove "bad" outcomes. The best output randomness gives different and interesting results, not good and bad results.
In one of my prototypes, there was very clear output randomness. You could try to use a skill, like Climbing. You'd roll a die and add your Climbing skill score. If the total was high enough, you succeeded. However, if you "failed", you learned from it, and your Climbing skill score increased by one.
If some results are better, make one or two outcomes stand out by being good, while the rest are mediocre. Don't have any "clearly bad" outcomes.
Even if you have good and bad results, avoid making them "strictly worse" results. This is where one result is equal or better in every way. Three goats might usually be better than two sheep, but three goats is strictly (always) better than two goats.
Randomness has some very positive attributes, and most games can benefit from a small amount of it.
Randomness makes each game different.
Chess starts out exactly the same each time, which is less interesting, and allows players to memorise opening sequences.
Randomness means a weaker player has a chance of beating a better player. This means that every game is a serious competition.
I'm an excellent Scrabble player, but anyone can beat me.
Randomness is exciting. Randomness is generally maligned in strategy games, but some games are about the surprise and excitement of randomness. For fun and light-hearted games, randomness is entirely appropriate. Also, if there's constant randomness, it tends to even out.