The best way I think about "proportionality" is rate of change. If a variable, alpha lets call it, and another variable, beta, are directly (I will explain inversely later) proportional it means as 1 increases the other will also increase, and as 1 decreases the other will also decrease. If 1 is doubled the other is doubled, and if 1 is halved the other is halved. It does not necessarily mean that if alpha is increased by 12 -just a random number for sake of explanation- that beta is also increased by 12. This is because 12 may hold a much larger stake in 1 variable than the other.

Now inverse proportionality is the exact opposite. If alpha and beta are inversely proportional then as 1 increases the other will decreased. when alpha is doubled beta would be halved but if alpha is increased by 12 (again) this still does not necessarily mean that beta is decreased by 12. Again this is because 12 may hold a much larger stake in alpha than beta.

To put this into a real world example. Consider a school where the number of students is directly proportional to the number of teachers - for sake of explanation lets say this ratio is for every 20 students there exists 1 teacher. If the school has 100 students ( so 5 teachers) and its student population this year increased by 20% to 120 students then so would the teacher population. Because 20% of 5 is 1, the new teacher count is 6. Its easily seen that the 20 students to every 1 teacher ratio is conserved between the previous and the current year. Now the question exists that if the school brings in 20 more students, does this mean that they also bring in 20 more teachers? No. Because 20 holds a much larger stake compared to the number of teachers than students (20 new teachers / 6 previous teachers > 20 new students / 120 previous students)

This was a pretty long example but I just wanted to make sure it was thorough.