An all-aspect missile is one which is able to track a target no matter which way the target faces relative to the missile. In other words, an all-aspect missile can be launched against a target in a tail-chase engagement

Tail-chase engagement

A tail-chase engagement is one where a surface-to-air missile system or jet aircraft engages another aircraft while the target aircraft is flying away from the attacker...

, in a head-on engagement

Head-on engagement

A Head-on engagement is one where a surface-to-air missile system or jet aircraft engages another aircraft while the target aircraft is flying towards the attacker. This makes engagement with infra-red homing missiles more difficult because the hot engine exhaust nozzle of the target are pointing...

, in a side-on engagement, from above, from below, etc.

This is opposed to older infrared homing

Infrared homing

Infrared homing refers to a passive missile guidance system which uses the emission from a target of electromagnetic radiation in the infrared part of the spectrum to track and follow it. Missiles which use infrared seeking are often referred to as "heat-seekers", since infrared is just below the...

 missiles which were only able to track the hot engine exhaust of an aircraft if the aircraft's engine exhaust was pointing towards the missile seeker, and thus were only successfully used in tail-chase engagements.

An example is the Israeli Rafael Advanced Defense Systems Python 5 air-air/ground-air missile.