|close-up of springtail/collembola|
These tiny critters are called springtails, or collembola, and they are not really insects at all but rather primitive soil micro-arthropods (a distinction that is only of interest to an entomologist!).
See Springtails In Homes & Gardens for more pictures and life history.
Springtails live in soil where they feed on bacteria, fungi, and occasionally plant roots. They are harmless to plants and even beneficial to healthy soils. Very large populations can build in highly organic soils. They are most often noticed following heavy rains when they are washed out of the soil by flooding and concentrate where rain water pools.
Springtails can enter homes when outside soils are saturated following heavy rains, or they can be brought in with house plant soil. Again, they are harmless and can be simply swept up when found. See the article cited above for more information.