Bonatus describes a besieged planet as one that separates from a malefic and applies to another (Con. 6). It shows a situation that is going from bad to worse.
William Lilly described a planet besieged as one that lies between the bodies of the two malefics Mars and Saturn. His example is Mars at 10 ° Aries, Venus 13° Aries, and Saturn 15° Aries. It is generally accepted that besiegement can occur by aspect as well as bodily conjunction. As a principle it refers to a planet trapped by hostile forces on either side.
The diagram shows William Lilly’s description of Venus besieged between the bodies of the two malefics: Mars and Saturn (CA, p.114).
NB: some older works refer to a contrasting condition - sometimes called 'bonification' or being 'bonified', where a planet is surrounded by contacts with benefic planets. See for example Johanne Schoener's list of scores for dignified and debilitated planets, where a planet surrounded by benefics receives five points, in contrast to a planet surrounded by malefics, which has five points taken away.