In soil, aeration refers to the extent of air gaps. Aerated soil will equate to happier plants with plenty of oxygen. That can be as important as water, sun, and nutrients. You can typically notice a lack of oxygen in the soil when you look at the plants’ roots. If the roots have an abnormal shape, this means that the soil is poorly aerated and too compact for your plants to develop properly. Undeveloped roots cause a chain reaction.
A spike aerator works fine to help with compaction, or simply sinking a shovel into the soil, lifting and leaving it in place. Garden beds should be mulched well. The mulch will also attract worms and microorganisms who like to feed on the organic matter, and this soil life naturally aerates. Rather than tilling, continue to add matter atop the garden bed.
As for container gardens, potted plants can be aerated with a chopstick. The pointy end of the chopstick should be shoved into the soil, and it will open up corridors for air and water to get in.