Brief explanation:

Strombolian eruptions are discrete explosions (called Strombolian explosions, Strombolian bursts etc.) of relatively fluid lava from a single vent. It is thought that they originate when large gas bubbles rising within the conduit burst at the partly solid surface of the magma column inside the vent.
They commonly occur on basaltic volcanoes such as Stromboli or Etna. Stromboli volcano in south Italy as the type example has given name to this kind of volcanic activity, because it has been in Strombolian activity for at least 2000 years. People have called Stromboli the "Lighthouse of the Tyrrhenian", since its frequent intermittent eruptions are during night visible from large distances. During Stromboli's most frequent activity, Strombolian explosions have occurred at one of its varying number of craters at intervals of 10-20 minutes, each lasting about 10-20 seconds.

Strombolian eruptions can vary widely in size. During powerful explosions, ejected lava lumps can reach up to 1000m altitude above the vent, whereas typical Strombolian explosions throw lava bombs a few tens to a 100-200m height. Weak Strombolian explosions only eject small amounts of coarse material and mainly release gasses and ash.
When the discrete Strombolian explosions during particularly violent phases merge into sustained jets of liquid lava, these eruptions are called lava fountains.

Powerful strombolian activity such as on the photo below left is often accompanied by the emission of lava flows.

Examples of Strombolian explosions on Stromboli volcano.

Below strombolian explosions on Etna volcano:

Powerful Strombolian explosions at Etna, in 2001 and 1999.