To bear witness, to testify, to affirm what one has seen, heard, or knows. Martyreō is courtroom language — giving sworn testimony. In the NT, it describes bearing witness to Christ, and from it comes our word 'martyr,' because early witnesses often died for their testimony.
The Christian faith is built on testimony: 'You will be my witnesses' (Acts 1:8). John's Gospel is structured around witnesses who testify to Jesus: John the Baptist, the Father, the works, the Scriptures, the Spirit. The ultimate test of testimony is willingness to die for it — hence martys came to mean 'martyr.' The blood of the martyrs is the seed of the church because their testimony proved costly and therefore credible.