Serious
Terrible, Very, Difficult, Hard, Hectic
A big change is a really serious thing. And people don't like change, either, making it a terrible event.
Also, in more recent history this has come to mean very as well.
たいへん
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.
日本語を習とくするのは大変ですが、がんばってくださいね。
Acquiring Japanese is difficult, but do your best!
大変丈夫な子供が生まれました。
They had a very healthy child.
災害時は、電話回線もネット回線も混み合って、繋がりづらくなるので、ブログの更新が大変です。
When there's a disaster, the phone and Internet circuits are overloaded and it gets hard to connect to them, so it's difficult to upload new blog posts.