What are Frequency and Oscillation?
Definition
The number of oscillations per unit time is called the frequency.
Explanation
Frequency is the same thing as oscillation count. Its unit is $\mathrm{Hz}$[Hertz], and it is commonly denoted by $f$, $\nu$, or $k$. $k \mathrm{Hz}$ means that it oscillates $k$ times per second. The period $T$ refers to the time it takes to oscillate once, so it has a reciprocal relationship with frequency.
$$ f = \frac{1}{T} $$
Angular Frequency
The angle rotated per unit time is called the angular frequency, commonly denoted by $\omega$. Its unit is $\mathrm{rad}$[radian]. It satisfies the following relationship with frequency.
$$ \omega = 2\pi f $$
Sampling Frequency
Sampling frequency refers to the interval at which a signal is measured, and by convention it is expressed as a frequency rather than a time. For example, if a signal is measured $2,000,000$ times in $1$ second, one says “the sampling frequency is $20\mathrm{MHz}( = 20 \times 10^{6}\mathrm{Hz})$.”