To invoke a spirit is to summon or draw a spirit being into your own body.
This is usually done to encourage communication between the spirit world and the material world and is part of many magico-religious practices.
The words invoke and evoke are often used synonymously, but Aleister Crowley notes the distinction:
To “invoke” is to “call in”, just as to “evoke” is to “call forth”. This is the essential difference between the two branches of Magick. In invocation, the macrocosm floods the consciousness. In evocation, the magician, having become the macrocosm, creates a microcosm.
~ Magick, Book 4, p.147