The mark of the beast is a symbolic identification for those who reject Christ and pledge total allegiance to the worldly systems of opposition against God. Throughout church history, perspectives on whether this is a literal physical mark or a spiritual counterfeit of God's sealing of His people have varied widely.
In Revelation 13:16-18, the beast requires a mark on the hand or forehead of all people, controlling their ability to buy or sell. Reformed theology often understands this imagery in light of the seal of God placed upon the foreheads of the 144,000 who follow the Lamb (Revelation 14:1). Just as the Old Testament covenant sign was to be a memorial upon the hand and between the eyes as a sign of dedication to Jehovah (Exodus 13:9), the mark of the beast represents a perverse, ultimate loyalty to the idols of this world rather than to the Lord Jesus Christ.
Rather than fostering fear or speculative guessing about technology, Scripture calls for the 'perseverance and faith of the saints' (Revelation 13:10) and those who keep the commandments of God and the faith of Jesus (Revelation 14:12). The ultimate mark of the believer is not one given by the beast, but the name of the Lamb and His Father written upon them by grace. Because you are more deeply accepted in Christ than you dared hope, you need not fear the threats of the beast; the Lamb has already overcome, and the wine of God's wrath is for those who refuse His gospel, not for those washed in His blood.