You have conducted a customer satisfaction research with a 5 point scale questions. The responses can be categorizes as follows:
120 out of 1000 (12%) have answered with Very satisfied
340 out of 1000 (34%) have answered with Satisfied
250 out of 1000 (25%) have answered with Neutral
190 out of 1000 (19%) have answered with Dissatisfied
100 out of 1000 (10%) have answered with Very dissatisfied
The bottom-two-box score is the combination of the two lowest categories. So you add up the number of respondents that have chosen either Very dissatisfied or Dissatisfied, in this case 290 respondents out of the total number of 1000 (=29%).
A lower bottom-box score means that a smaller part of your respondents is (very) negative in their answer.