The single most common print complaint is "the colour is not what I saw on screen". It is almost always the same cause, and it is avoidable.
They are different kinds of colour
Your screen emits light. Red, green and blue light added together make white. A press puts ink on paper, and ink subtracts light — cyan, magenta, yellow and black layered together approach a muddy dark. Two opposite systems, so they cannot cover the same range of colours.
RGB reaches colours CMYK simply cannot make. Electric blues, neon greens, vivid oranges. When you convert, those colours fall back to the nearest printable equivalent, and the drop is visible.
What actually goes wrong
Bright blue turning purple. The classic. A saturated screen blue has no CMYK equivalent and lands somewhere violet.
Vivid green going flat. Same reason.
Black looking washed out. Large areas of 100% K alone look grey next to the page. Use a rich black — a common recipe is around 60C 40M 40Y 100K — for big solid areas, but keep small text at 100% K only, or it fringes when the plates shift a fraction.
The same file printing differently at two shops. Different presses, papers and profiles. This is why you ask for the shop specification instead of assuming.
Rules I work by
Decide the destination first. Print job, start the document in CMYK. Screen only, stay in RGB and never convert.
Convert yourself, do not let the RIP do it. If you send RGB, the press software converts blindly and you find out at delivery. Convert while you can still adjust.
Check your brand colours in both. Every identity should carry a CMYK build, an RGB or HEX value, and ideally a Pantone reference. Deliver all three so nobody has to guess.
Use a spot colour when exactness matters. If the brand lives or dies on one precise colour, a Pantone ink prints it consistently. It costs more, and sometimes it is worth it.
Never trust an uncalibrated monitor. Your screen is a suggestion. For anything critical, ask for a proof from the actual printer.
The short version
Work in the colour space of the thing you are making, convert deliberately rather than accidentally, and get a proof before a large run. Five minutes of caution beats reprinting five thousand flyers.