A periodic waveform is a waveform that continually repeats the exact same shape. How often it repeats is known as its frequency, and in the case of audio-range frequencies in particular, it's also known as its pitch.
An oscillator can generate periodic waveforms at audio-range frequencies (roughly 20 Hz to 20 kHz). An LFO can generate them at infrasonic frequencies (less than roughly 20 Hz).
The most common periodic waveforms made by oscillators and LFOs are the sine wave, triangle wave, sawtooth wave, and pulse wave. The square wave is a pulse wave of a specific width.
Using additive synthesis, a periodic waveform can be made using only harmonics (various sine waves at multiples of its frequency).