the dielectric constant

Take two metal plates a fixed distance apart and connect them to a battery: they hold a certain amount of charge. Now slide a slab of the right material — a dielectric — into the gap without changing anything else, and the plates suddenly hold much more charge at the same voltage. The dielectric constant is simply the number that says how much more. It is the single most important number for a capacitor material.

Formally the dielectric constant, also called the relative permittivity and written epsilon_r, is the ratio of the capacitance you get with the material filling the gap to the capacitance of the same empty (vacuum) gap: epsilon_r = C_material / C_vacuum. Vacuum is defined as exactly 1, dry air is about 1.0006, ordinary insulating ceramics like alumina sit near 9 to 10, and the ferroelectric titanates that fill capacitors reach 1000 to over 10000. The extra charge comes from the material's own charges shifting a little in the field — its polarization — which pulls more charge onto the plates to balance it. In the governing relation D = epsilon_0 epsilon_r E, the electric displacement D (surface charge per area) is the applied field E amplified by epsilon_r, with epsilon_0 the permittivity of free space.

A high dielectric constant is what lets an entire microfarad of capacitance hide inside a chip smaller than a grain of rice, so barium-titanate-based ceramics with epsilon_r in the thousands are the heart of the multilayer ceramic capacitor. But a crucial honesty: in these high-value ferroelectric ceramics epsilon_r is not really constant at all — it swings by tens of percent with temperature, drifts down with age, and drops under a DC bias voltage. That is why capacitor makers split ceramics into Class I (low epsilon_r near 20 to 100, but rock-stable, the C0G/NP0 grades used where the value must not move) and Class II (high epsilon_r, far more capacitance per volume, but temperature- and voltage-dependent, the X7R and Y5V grades). You buy capacitance with instability.