Period is how much history the maths uses
SMA(50) averages the last 50 bars. RSI(14) compares gains and losses over the last 14 bars. ATR(14) averages the true range over the last 14 bars. The number is simply how many bars the calculation looks back over.
Two consequences follow directly. A short period reacts fast and is noisy — it will whipsaw you in chop. A long period is smooth and stable, but it lags badly and you will be late on turns. There is no correct setting, only a trade-off you choose deliberately.
Period is counted in bars, not in time
This is the bit that catches people. A 200-period moving average on a five-minute chart covers 200 five-minute bars — about 17 hours of trading. A 200-period moving average on a daily chart covers roughly ten months. Same number, completely different meaning.
So the useful question is never "what period should I use" but "how much market history do I want this to summarise, on the time frame I am trading?" If you want roughly the last quarter on a daily chart, you want about 60 periods. If you want the last week on an hourly chart, you want about 40 (allowing for the sessions your market actually trades).
Why the popular defaults exist
14 for RSI and ATR, 20 for Bollinger Bands with 2 standard deviations, 12/26/9 for MACD, 50 and 200 for moving averages. None of these is optimal; they are conventions left over from when these tools were designed for weekly charts on paper. They persist because using the same numbers as everyone else has a mild self-fulfilling benefit — if enough people watch the 200-day, it tends to matter. That is a reason to know the defaults, not a reason to think they were derived for your market.
Changing the number is not tuning an edge
Beginners who discover the parameter box usually spend a while searching for the magic setting that would have worked on the last few months. This is curve fitting, and it does not survive contact with next month. Pick a period that matches the amount of history you want to summarise, write down why, and then leave it alone so your readings stay comparable week to week.
How to check this yourself
Put three moving averages on one chart: SMA(10), SMA(50) and SMA(200). Watch how far each one trails behind a sharp reversal. Then switch the chart from daily to hourly without touching the periods, and watch the same three lines change meaning entirely — the 200 goes from "ten months of context" to "about a week and a half". That single experiment teaches more about parameters than any amount of reading.