An amplification factor is a metric, the ratio that a thorough DDoS test uses to quantify how much a reflection vector multiplies an attacker's bandwidth. It is the size of the response a server returns divided by the size of the spoofed request that triggered it. A DNS open resolver might return 50x the query size; memcached on UDP 11211 has been measured above 50,000x. The higher the factor, the less upstream bandwidth an attacker needs to saturate a target link.
Why it matters in DDoS testing
Amplification factor predicts the bits-per-second a given pool of reflectors can deliver, which sets the volumetric ceiling a test should provision toward. It also ranks which exposed services (DNS, NTP, CLDAP, SSDP, memcached) pose the largest reflection risk if left reachable. A test characterizes whether ingress filtering and BCP 38 actually deny spoofed source traffic before it can be reflected.
The reflection vectors behind this metric are detailed in Understanding DDoS Attack Vectors.