It means that we note the impact of the experience on our senses and our thoughts without denial, without turning away and without engaging in a mental drama about it.
Suppose I have agreed to give a presentation to work colleagues next week. Suppose also that I notice a ball of tension in my stomach whenever I think about the presentation.
Acceptance means I choose to experience that ball of anxiety without getting into a drama (OMG what if my boss is there, what if I stumble over my words, what if everyone notices I'm blushing?), without denial and without turning away.
In acceptance I refuse to waste energy fighting with that ball of anxiety. Instead I allow myself to experience my anxiety while I do what needs to be done, namely to prepare my presentation.
Usually, the acceptance in itself reduces the anxiety. And when I go on to do the preparation, the anxiety will usually reduce further. Sometimes the anxiety stays - but acceptance means I am not adding to it through generating pointless fearful thoughts that make matters worse while achieving nothing.