What does it mean that the Holy Spirit proceeds from the father and son by spiration?
Spiration is the act of breathing. The Holy Spirit proceeds from the Father and the Son in this unique way. For example, when Jesus appeared to the disciples after his resurrection he “breathed” the Holy Spirit on them. This is recorded in John 20:22: “he breathed on them, and said to them, ‘Receive the Holy Spirit’”.
For more information on this see the Catholic Encyclopedia article: Holy Ghost