Threshold voltage

The threshold voltage $V_t$ is the minimum gate-to-source voltage $V_{GS}$ at which a conducting MOSFET channel forms. Below it the device is off; above it a channel exists and the transistor can pass current.

What it physically marks

In an n-MOSFET the gate sits over p-type substrate, separated by the Gate oxide. Raising $V_{GS}$ from zero first only repels holes from the surface and exposes a depletion region — still no channel, still no current. Keep raising it and eventually the surface attracts enough electrons to invert it: a thin layer of mobile electrons forms right under the oxide, connecting source to drain. The exact $V_{GS}$ at which that inversion layer first appears is $V_t$. So $V_t$ is the dividing line between “the gate is just pushing charge around in the substrate” and “the gate has built a real channel.”

For modern silicon n-MOSFETs $V_t$ is typically $0.3\text{V}$ to $1\text{V}$.

Overdrive: how far past threshold you are

Knowing you are above $V_t$ is not enough — how far above sets how strong the channel is. That excess is the Overdrive voltage:

$V_{OV}=V_{GS}-V_t$

Here $V_{GS}$ is the applied gate-to-source voltage and $V_t$ the threshold. Every drain-current formula (triode and square-law) is written in terms of $V_{OV}$, not $V_{GS}$ directly, because it is the overdrive that physically controls the channel charge.

p-MOSFET: negative threshold

For a p-MOSFET everything mirrors. Its threshold $V_{tp}$ is negative — typically around $-0.5\text{V}$. You turn the device on by making $V_{GS}$ negative enough that $V_{GS}<V_{tp}$. The clean bookkeeping trick is to work in magnitudes: a p-MOSFET conducts when $|V_{GS}|>|V_{tp}|$, exactly paralleling the n-MOSFET condition $V_{GS}>V_t$.

Threshold is not a fixed constant

$V_t$ is a process-dependent parameter that varies between nominally identical transistors, drifts with temperature, and — importantly — is raised by the Body effect: if the body (substrate) is held below the source ($V_{BS}<0$), the sub-channel depletion region widens and the gate must work harder, so the effective $V_t$ increases. This spread is exactly why fixing $V_{GS}$ is a terrible way to bias a MOSFET (see MOSFET biasing); robust schemes use Negative feedback so the operating point depends on stable resistors instead of the wobbly $V_t$.