Engage gives the Digimon an optional attack at the end of your turn, on top of anything it already did. In practice that's a second wave your opponent has to plan around after your normal attacks resolve. Decks use it to stack extra security checks or to force blocks at a moment when the defensive options are already spent.
16-44-1. <Engage> is a keyword effect where a Digimon with this effect may attack at the end of your turn. 16-44-2. <Engage> is a trigger-type effect that triggers at the End of Your Turn timing. (For details, refer to 15-8-3 "Trigger-Type Effects") 16-44-3. The processing from <Engage> is optional.
Comprehensive Rules §16-44 — official rules page
3 cards carry this keyword:
Rule text © Bandai, quoted from the official Comprehensive Rules for reference. Combalo is not affiliated with Bandai.