What the image is
A superheterodyne receiver mixes the incoming signal with a local oscillator (LO) to produce a fixed intermediate frequency (IF), where most of the filtering and gain happen. The mixer responds to any signal that's one IF away from the LO, on either side. One of those is the wanted signal and the other is the image, two IFs away. Unless the filtering before the mixer removes it, a signal on the image frequency comes through just as if you were tuned to it.
Why IFs are chosen as they are
A higher IF puts the image further away, where the front-end filter can reject it more easily. That's why VHF receivers use 10.7 MHz or more, and modern HF rigs and scanners use first IFs of 45 or 70 MHz, well above the band they receive, so the image is far outside it. Lower IFs, such as 455 kHz, give sharp selectivity, so many receivers use two or three conversions to get both.
For blocking strong signals before the mixer, see the bandpass filter calculator, and for spurious products from your own transmitter, the harmonics calculator.
Questions
What is the image frequency formula?
With the LO above the signal, image = signal + 2 × IF. With the LO below, image = signal − 2 × IF.
What is the image of 145.5 MHz with a 10.7 MHz IF?
With a high-side LO at 156.2 MHz, the image is 166.9 MHz.
How is image rejection improved?
With better filtering before the mixer, or a higher first IF so the image is further away.
Do SDRs have images?
Direct-sampling SDRs have aliases instead, and some tuner-based SDRs such as the RTL-SDR have image responses too, which a filter helps with.