This is called gating, and it's in another comment too. They use the same technique in other types of heart imaging as well as most are very motion sensitive.

I work in CT not MRI but in CT gating works by having the patient hooked up to an ECG machine that communicates with the CT computer, the computer assesses the patients heart rate while doing some breath hold exercises and gives a range of rates that it think the patients heart will be beating at during the duration of the scan. Then you can do two things, one is retrospective gating or prospective gating.

Retrospective gating scans the patient during their whole heart cycle from heart at rest to heart at rest again, and then takes all of that data to rebuild you a picture of the heart where the computer thinks it will be the most still. With this type of scanning you can go back and reconstruct better phases if the computer didnt end up making you the best possible images but it comes at the cost of radiating the patient when it is potentially unessessary and having a longer exposure time with increases overall dose to the patient.

With prospective gating you are only scanning when the computer thinks the patients heart is at rest, or in between beats, when the heart is the most still. With this type of scanning you have more limited reconstruction options because you have less scan time and less raw data but the patient receives less radiation dose.

Disclaimer that radiation does is not relevant to the MR imaging because magnetic resonance is not ionizing radiation.

Also, I am just learning cardiac scanning so feel free to point out any errors if there is someone in the comments with more experience!