Solder paste is used for joint formation in reflow soldering. The paste consists of solder particles bonded by a flux. Although this is a simplification, basically that's the system that is deposited at the joint areas before soldering. The solder lumps should be deposited as a coherent dot without loose particles.
In most cases solder paste is deposited by a screen printing process. The paste should be so deposited that it behaves as one small lump of paste forever joint. If in this process some paste is deposited outside that lump it can form solitaire solder balls as the paste starts to melt. Also the paste should be deposited on the metal part that should be soldered. If paste is deposited outside the joint area it might not be able to be part of the solder joint.
The lump might also be separated by the placement of the component in the solder paste. Displaced paste particles might in that case not be able to coalesce with the original lump and create a separate solder ball.
Too high amount of paste at the connection
It is also possible that the solder paste during the placement of the component is squeezed underneath a chip component. During reflow this paste will then create a solder ball that is squeezed out from the side of the gap between component body and substrate.
Another reason for solder ball formation might be that the paste contains too much oxide. In that case the flux is unable to melt all the solder particles together and a ring of often small satellites will surround the solder joint.
If during the solder process in the preheat stage the temperature rises at a too high rate, the volatiles from the flux will escape so fast that they can displace the solder particles, so that they will separate from the original lump. These solder particles will during melting create separate solderballs.
Should solder balls be removed?
According to the ANSI/IPS-S-815B document § 3.6.6 solder balls are allowed if not greater then 0.13 mm diameter. They should not violate minimum electrical conductor spacings and the amount of solder balls should not exceed five per square inch. If we assume that the maximum solder ball is adhering then this ball has a weight of 1.15 microgram. The adhesion force is normally much stronger than the weight of the solder ball, which makes it difficult to remove them with brushes. This is especially the case when there are also SMD's on the solder side. The brushes may then not even touch the solder ball. A matter of even greater concern is where do the solder balls go? They may be wiped underneath components where they are just fixed in a wedged gap. During operation of the board this gap will change due to thermal expansions. This may give pressure on the solder ball and this may cause damage to the solder resist. What is underneath? Another possibility is that the ball comes free, now what will it do? It is good to know that such small solder balls that are fixed to the solder resist can withstand an acceleration of 40g, before they get loose from the solder resist. All together it is more safe to leave the allowed balls where they are, or better, prevent their formation by optimizing the process.