This is an intentionally very open ended question. What does it mean for an antenna to be a 50-ohm antenna at some frequency? How do you make a 50-ohm antenna for say 433.92MHz? What are the options? What are the consequences of it being different from 50-ohms?
Trying to think what 433 is used for off the top of my head :) Is that the weak signals band?
At any rate, most 2-way radios are made to match up to a 50ohm antenna and the matching is left up to you. You can get an antenna that is already tuned, or you can do impedence matching through a number of techniques (see the referenced article below).
With a good match, you reduce standing waves. Standing waves build up when the radio sends out a nicely modulated signal but the antenna isn't resonating at that frequency and causes standing waves, which feed right back into the radio and can blow out the final stage.
The higher the output power, the more this becomes important. At very low power, say <1watt, the worst you have to worry about is the antenna not resonating and your signal not going anywhere. At higher powers, say 50+ watts, you can damage your transmitter in less than 1 second. Modern radios have built-in SWR detectors that will cut the power if it detects a problem. Those aren't always guaranteed to work though.
When referring to RF equipment you have to deal with 'characteristic impedance', which is a property of antennas, feed lines, and even transmitter output stages.
The important thing is to make sure that impedances are matched up all the way from the equipment to the antenna. This is more important for transmitters, since more power is involved, but doesn't hurt for receivers either.
One thing you don't want to do is just wire together two items with different impedances. There are RF transformers of various kinds can be used to match up sections that otherwise would be mismatched. Any abrupt change in impedance causes RF energy encountering the mismatch to partially reflect, sort of like what happens when light strikes a piece of glass. When one end of the system is a 100W transmitter, this can result in significant energy being reflected back to the tranmitter's output stage. Basically, it's just inefficient, since the reflected energy just becomes waste heat in the transmitter, and the output from the antenna is diminished. The measure of how much reflection is going on is referred to as the standing wave ratio, often abbreviated SWR.
Not all RF systems are 50 ohms. There are kinds of coax (e.g. RG-59) that are 75 ohms, and 300 ohm twin lead that are not uncommon.
A great tutorial: The Dropout’s Guide to PCB Trace Antenna Design
It's also useful to understand why a 50-ohm antenna is so important.
Let's say you have a source with an output impedance (resistance) of 50 ohms, like the ideal battery/resistor combination in the following diagram:
If you want to extract maximum power from the above source, the load resistor you need has to be 50 ohms. Try it yourself - put in 40, 50, and 60 ohms, and calculate how much power goes to the load in each case.
So, this is the reason why 50 ohm antennas are important: The sources that drive them typically have 50 ohms of impedance.
Therefore, if you want to deliver the most RF power from your 50-ohm source to your antenna - voila, only a 50 ohm antenna will do that!
Here's a good app note for making a Bluetooth PCB antenna (2.4Ghz)
50 Ohm is input impedance of feedline to the antenna. In general practice, we connect an antenna with 50 Ohm connector ( like SMA, Coax...) so feedline impedance should be also 50 Ohm.
For Bluetooth antenna design at 2.4 GHz, you can also refer https://anilkrpandey.wordpress.com/2017/01/19/inverted-f-bluetooth-antenna-design-for-smart-phone/