This is one way to express a percentage or amount. "One in five" means 20%. "One in ten" means 10%.

Saying numbers this way usually makes them easier for people to understand them.

Notice that in the example, the speaker says "one in five families has...". The verb agrees with "one":

(one) has trouble...

(one in five) has trouble...

(one in five families) has trouble...

However, you may also hear some English speakers say "one in five families have trouble...". This isn't considered correct grammar, but people speak this way anyway sometimes.